Non-metric Connection Research Articles

NON-EXISTENCE OF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE KAEHLER MANIFOLDS ADMITTING NON-METRIC π-CONNECTIONS

Abstract. In this paper, we study two types 1-lightlike submanifoldsM, so called lightlike hypersurface and half lightlike submanifold, of anindefinite Kaehler manifold M¯ admitting non-metric π-connection. Weprove that there exist no such two types 1-lightlike submanifolds of anindefinite Kaehler manifold M¯ admitting non-metric π-connections. 1. IntroductionA linear connection ∇¯ on a semi-Riemannian manifold (M,¯ ¯g) is called anon-metric π-connection if, for any vector fields X, Y and Z on M¯, it satisfies(1.1) (∇¯ X g¯)(Y,Z) = −π(Y )¯g(X,Z)−π(Z)¯g(X,Y ),where π is a 1-form, associated with a non-vanishing smooth vector field ζ onM¯ by π(X) = ¯g(X,ζ). We say that ζ is the characteristic vector field of M¯.Two special cases are important for both the mathematical study and theapplications to physics: (1) A non-metric π-connection ∇¯ on M¯ is called asemi-symmetric non-metric connection if its torsion tensor T¯ satisfiesT¯(X,Y ) = π(Y )X −π(X)Y.The notion of semi-symmetric non-metric connections on a Riemannian man-ifold was introduced by Ageshe and Chafle [1] and later studied by many au-thors. The lightlike version of Riemannian manifolds with semi-symmetricnon-metric connections have been studied by some authors [15, 16, 17, 18, 23].(2) A non-metric π-connection ∇¯ on M¯ is called a quarter-symmetric non-connection if its torsion tensor T¯ satisfiesT¯(X,Y) = π(Y )φX −π(X)φY,where φ is a (1,1)-type tensor field. In particular, if φX = X, then the quarter-symmetric connection reduces to the semi-symmetric connection [8]. Thus the

SINGULAR THEOREMS FOR LIGHTLIKE SUBMANIFOLDS IN A SEMI-RIEMANNIAN SPACE FORM

Abstract. We study the geometry of lightlike submanifolds of a semi-Riemannian manifold. The purpose of this paper is to prove two singulartheorems for irrotational lightlike submanifolds M of a semi-Riemannianspace form M(c) admitting a semi-symmetric non-metric connection suchthat the structure vector eld of M(c) is tangent to M. 1. IntroductionThe theory of lightlike submanifolds is an important topic of research indi erential geometry due to its application in mathematical physics, especiallyin the general relativity. The study of such notion was initiated by Duggal andBejancu [3] and later studied by many authors (see up-to date results in twobooks [4, 7]). Recently many authors have studied lightlike submanifolds Mof inde nite almost contact metric manifolds M (see [5, 6, 7, 8, 14, 16]). Theauthors in above papers principally assumed that the structure vector eld of M is tangent to M. Calin proved the following result in his thesis:Calin’s result [2]: If the structure vector eld of M is tangent to M, thenit belongs to the screen distribution S(TM) of M.After Calin’s work, many earlier works [5, 6, 7, 14, 16], which have been writ-ten on lightlike submanifolds of inde nite almost contact metric manifolds,obtained their results by using the Calin’s result described in above.The notion of a semi-symmetric non-metric connection on a Riemannianmanifold was introduced by Ageshe and Chae [1]. Although now we havelightlike version of a large variety of Riemannian submanifolds, the geometry oflightlike submanifolds of semi-Riemannian manifolds admitting semi-symmetricnon-metric connections has been few known. Several works ([9]˘[13]), whichhave been written on lightlike submanifolds of semi-Riemannian manifolds ad-mitting semi-symmetric non-metric connections, also obtained their results by

ASCREEN LIGHTLIKE HYPERSURFACES OF A SEMI-RIEMANNIAN SPACE FORM WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

Abstract. We study lightlike hypersurfaces of a semi-Riemannian spaceform fM(c) admitting a semi-symmetric non-metric connection. First, weconstruct a type of lightlike hypersurfaces according to the form of thestructure vector field of Mf(c), which is called a ascreen lightlike hyper-surface. Next, we prove a characterization theorem for such an ascreenlightlike hypersurface endow with a totally geodesic screen distribution. 1. IntroductionThe theory of lightlike submanifolds is an important topic of research in dif-ferential geometry due to its application in mathematical physics, especially inthe electromagneticfield theory. The study ofsuch notion wasinitiated by Dug-gal and Bejancu [3] and later studied by many authors (see up-to date resultsin two books [4, 5]). The notion of a semi-symmetric non-metric connectionon a Riemannian manifold was introduced by Ageshe and Chafle [1]. Recentlyseveral authors ([9]-[13]) studied lightlike hypersurfaces in a semi-Riemannianmanifold admitting a semi-symmetric non-metric connection. Most of authorsthat wrote on either lightlike hypersurfaces M of semi-Riemannian manifoldsMfadmitting semi-symmetric non-metric connections or lightlike hypersurfacesM of indefinite almost contact manifolds Mffail to treat with the case the struc-ture vector field ζ of Mfis not tangent to M, but studied only to the case ζis tangent to M (such M is called tangential lightlike submanifold ([9]-[13]) ofMf). There are few papers on non-tangential lightlike submanifolds of indefinitealmost contact manifolds studied by Jin ([6]-[8]).In this paper, we study non-tangential lightlike hypersurfaces of a semi-Riemannian space form admitting a semi-symmetric non-metric connection.There are several different types of non-tangential lightlike hypersurfaces ac-cording to the form of the structure vector field of the ambient manifold. We

NON-TANGENTIAL HALF LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN MANIFOLDS WITH SEMI-SYMMETRIC NON-METRIC CONNECTIONS

In this paper, we construct two types of non-tangential half lightlike submanifolds of a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. Our main result is to prove several characterization theorems for each types of such half lightlike submanifolds equipped with totally geodesic screen distributions.

HALF LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN SPACE FORM WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

In this paper, we study screen quasi-conformal irrotational half lightlike submanifolds M of a semi-Riemannian space form <TEX>$\tilde{M}(c)$</TEX> admitting a semi-symmetric non-metric connection, whose structure vector field <TEX>${\zeta}$</TEX> is tangent to M. The main result is a classification theorem for such Einstein half lightlike submanifolds of a Lorentzian space form admitting a semi-symmetric non-metric connection.

CR-submanifolds of a nearly trans-hyperbolic Sasakian manifold with a quarter symmetric non-metric connection

This paper deals with the study of CR-submanifolds of a nearly trans-hyperbolic Sasakian manifold with a quarter symmetric non-metric connection. We study parallel distribution relating to

On semi-invariant submanifolds of a nearly Sasakian manifold with a quarter symmetric non-metric connection

On semi-invariant submanifolds of a nearly Sasakian manifold with a quarter symmetric non-metric connection

Some Properties of &amp;lt;i&amp;gt;CR&amp;lt;/i&amp;gt;-Submanifolds of a Nearly Trans-Sasakian Manifold with a Semi Symmetric Non-Metric Connection

This paper deals with the study of CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric non-metric connection. Nijenhuis tensor, integrability conditions for some distributions on CR-submanifolds of a nearly trans-Sasakian manifold with a semi symmetric non- metric connection are discussed.

TWO CHARACTERIZATION THEOREMS FOR IRROTATIONAL LIGHTLIKE GEOMETRY

We study irrotational half lightlike submanifolds M of a semi-Riemannian space form with a semi-symmetric non-metric connection such that its structure vector field is tangent to M. We prove two characterization theorems for such an irrotational half lightlike submanifold.

CURVATURE OF MULTIPLY WARPED PRODUCTS WITH AN AFFINE CONNECTION

In this paper, we study the Einstein multiply warped prod- ucts with a semi-symmetric non-metric connection and the multiply warp- ed products with a semi-symmetric non-metric connection with constant scalar curvature, we apply our results to generalized Robertson-Walker spacetimes with a semi-symmetric non-metric connection and generalized Kasner spacetimes with a semi-symmetric non-metric connection and find some new examples of Einstein affine manifolds and affine manifo lds with constant scalar curvature. We also consider the multiply warped products with an affine connection with a zero torsion.

TWO CHARACTERIZATION THEOREMS FOR LIGHTLIKE HYPERSURFACES OF A SEMI-RIEMANNIAN SPACE FORM

We study lightlike hypersurfaces M of a semi-Riemannian space form <TEX>$\tilde{M}(c)$</TEX> with a semi-symmetric non-metric connection whose structure vector field is tangent to M. Our main result is two characterization theorems for such a lightlike hypersurface.

Einstein half lightlike submanifolds of a Lorentzian space form with a semi-symmetric non-metric connection

We study screen conformal Einstein half lightlike submanifolds M of a Lorentzian space form �(c) of constant curvature c admitting a semi-symmetric non-metric connection subject to the conditions; (1) the structure vector field ofis tangent to M, and (2) the canonical normal vector field of M is conformal Killing. The main result is a characterization theorem for such a half lightlike submanifold. MSC: 53C25; 53C40; 53C50

EINSTEIN LIGHTLIKE HYPERSURFACES OF A LORENTZ SPACE FORM WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

We study Einstein lightlike hypersurfaces M of a Lorentzian space form f M(c) admitting a semi-symmetric non-metric connection sub- ject to the conditions; (1) M is screen conformal and (2) the structure vector fieldof f M belongs to the screen distribution S(TM). The main result is a characterization theorem for such a lightlike hypersurface.

A CLASSIFICATION OF HALF LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

In this paper, we study the geometry of half lightlike submanifolds M of a semi-Riemannian manifold <TEX>$\tilde{M}$</TEX> with a semi-symmetric non-metric connection subject to the conditions; (1) the characteristic vector field of <TEX>$\tilde{M}$</TEX> is tangent to M, the screen distribution on M is totally umbilical in M and the co-screen distribution on M is conformal Killing, or (2) the screen distribution is integrable and the local lightlike second fundamental form of M is parallel.

Almost Hermitian manifold with a Generalised type of non-metric connection

The main aim of the present paper is to study a unique Generalised type of Non-Metric Connection in an almost Hermitian manifold. This connection unifies the different types of Semi-Symmetric Non-Metric and Symmetric Non-Metric connections in an almost Hermitian manifold.

ON A QUARTER SYMMETRIC NON-METRIC CONNECTION IN A KENMOTSU MANIFOLDS

In this paper we study a quarter-symmetric non-metric connection in a Kenmotsu manifold. AMS Subject Classification: 58D17, 57R15

On a Hsu-Unified Structure Manifold with a Quarter-Symmetric Non-Metric Connection

In the present paper, we have defined a Hsu-unified structure manifold and a Hsu-Kahler manifold and studied some properties of the quarter-symmetric non-metric connection. Certain interesting results on such manifolds have been obtained. We have also studied the properties of the contravariant almost analytic vector field on these manifolds equipped with the quarter-symmetric non-metric connection.

Some properties of a semi-symmetric non-metric connection on a Sasakian manifold

The object of the present paper is to study some properties of semi-symmetric non-metric connection on a Sasakian manifold. Mathematics Subject Classification: 53C15, 53C25

CR-submanifolds of a Lorentzian para-Sasakian manifold endowed with a semi-symmetric non-metric connection

CR-submanifolds of a Lorentzian para-Sasakian manifold endowed with a semi-symmetric non-metric connection

Quarter-Symmetric Nonmetric Connection onP-Sasakian Manifolds

The object of the present paper is to study a quarter-symmetric nonmetric connection on aP-Sasakian manifold. In this paper we consider the concircular curvature tensor and conformal curvature tensor on aP-Sasakian manifold with respect to the quarter-symmetric nonmetric connection. Next we consider second-order parallel tensor with respect to the quarter-symmetric non-metric connection. Finally we consider submanifolds of an almost paracontact manifold with respect to a quarter-symmetric non-metric connection.