Indefinite Kenmotsu Manifolds Research Articles

Totally contact umbilical screen-slant and screen-transversal lightlike submanifolds of indefinite Kenmotsu manifold

Totally contact umbilical screen-slant and screen-transversal lightlike submanifolds of indefinite Kenmotsu manifold

Geometry of Indefinite Kenmotsu Manifolds as *η-Ricci-Yamabe Solitons

In this paper, we study the properties of ϵ-Kenmotsu manifolds if its metrics are *η-Ricci-Yamabe solitons. It is proven that an ϵ-Kenmotsu manifold endowed with a *η-Ricci-Yamabe soliton is η-Einstein. The necessary conditions for an ϵ-Kenmotsu manifold, whose metric is a *η-Ricci-Yamabe soliton, to be an Einstein manifold are derived. Finally, we model an indefinite Kenmotsu manifold example of dimension 5 to examine the existence *η-Ricci-Yamabe solitons.

η-Ricci-Yamabe solitons on submanifolds of some indefinite almost contact manifolds

In this paper, we study the η-Ricci-Yamabe soliton on invariant and anti-invariant submanifolds of indefinite Sasakian manifolds, indefinite Kenmotsu manifolds and indefinite trans-Sasakian manifolds concerning Riemannian connection and quarter symmetric metric connection.

Symmetries in lightlike hypersufaces of indefinite Kenmotsu manifolds

Symmetries in lightlike hypersufaces of indefinite Kenmotsu manifolds

Almost Weyl structures on null geometry in indefinite Kenmotsu manifolds

Abstract We introduce and investigate a new concept of almost Weyl structures on null hypersufaces in indefinite Kenmotsu manifolds, tangent to the structure vector field. We show that, under some conditions, there are foliations on almost Weyl null hypersufaces which are Einstein-Weyl with scalar curvature of constant sign.

EQUIVALENCE CONDITIONS OF SYMMETRY PROPERTIES IN LIGHTLIKE HYPERSURFACES OF INDEFINITE KENMOTSU MANIFOLDS

The paper deals with lightlike hypersurfaces which are locally symmetric, semi-symmetric and Ricci semi-symmetric in indefinite Kenmotsu manifold having constant <TEX>$\bar{\phi}$</TEX>-holomorphic sectional curvature c. We obtain that these hypersurfaces are totally goedesic under certain conditions. The non-existence condition of locally symmetric lightlike hyper-surfaces are given. Some Theorems of specific lightlike hypersurfaces are established. We prove, under a certain condition, that in lightlike hyper-surfaces of an indefinite Kenmotsu space form, tangent to the structure vector field, the parallel, semi-parallel, local symmetry, semi-symmetry and Ricci semi-symmetry notions are equivalent.

A Conformal Connection on Null Hypersurfaces of Indefinite Kenmotsu Manifolds

In this paper, our main remark is that proper totally contact umbilical integral manifolds of screen integrable null hypersurfaces in indefinite Kenmotsu manifolds admit \(\eta \)-Weyl structures. Its geometry is closely related to the one of a normal subbundle over the indefinite Kenmotsu manifold.

Totally contact umbilical slant lightlike submanifolds of indefinite Kenmotsu manifolds

In this paper, we study totally contact umbilical slant lightlike submanifolds of indefinite Kenmotsu manifolds. We prove that there does not exist totally contact umbilical proper slant lightlike submanifold in indefinite Kenmotsu manifolds other than totally contact geodesic proper slant lightlike submanifold. We also prove that there does not exist totally contact umbilical proper slant lightlike submanifold of indefinite Kenmotsu space forms. Finally, we give some characterization theorems on minimal slant lightlike submanifolds of indefinite Kenmotsu manifolds.

Non existence of totally contact umbilical GCR-lightlike submanifolds of indefinite Kenmotsu manifolds

In present paper, after finding the conditions for the integrability of various distributions of a GCR-lightlike submanifold of indefinite Kenmotsu manifolds, we prove that there do not exist totally contact umbilical GCR-lightlike submanifolds of indefinite Kenmotsu manifolds other than totally contact geodesic GCR-lightlike submanifolds and moreover it is a totally geodesic GCR-lightlike submanifold. 2000 AMS Classification: 53C15, 53C40, 53C50.

Non-existence of screen homothetic lightlike hypersurfaces of an indefinite Kenmotsu manifold

We study screen homothetic lightlike hypersurfaces M of an indefinite Kenmotsu manifold M with flat transversal connection. We prove that there do not exist screen homothetic lightlike hypersurfaces of indefinite Kenmotsu manifolds with flat transversal connection subject to the conditions: (1) M is locally symmetric, or (2) M is semi-symmetric. Mathematics Subject Classification: 53C25, 53C40, 53C50

TWO CHARACTERIZATION THEOREMS FOR HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE KENMOTSU MANIFOLD

In this paper, we study the curvature of locally symmetric or semi-symmetric half lightlike submanifolds M of an indefinite Kenmotsu manifold , whose structure vector field is tangent to M. After that, we study the existence of the totally geodesic screen distribution of half lightlike submanifolds of indefinite Kenmotsu manifolds with parallel co-screen distribution subject to the conditions: (1) M is locally symmetric, or (2) the lightlike transversal connection is flat.

Submanifolds of some indefinite contact and paracontact manifolds

The purpose of the present paper is to study some types of submanifolds of indefinite contact and paracontact manifolds and a few properties of contact CR-submanifolds of an indefinite Sasakian manifold, indefinite Kenmotsu manifold, indefinite trans-Sasakian manifold and ε-paracontact Sasakian manifold.

On Parallelism of Half-Lightlike Submanifolds of Indefinite Kenmotsu Manifolds

We mainly investigate the parallelism of half-lightlike submanifolds of indefinite Kenmotsu manifolds. It is proved that a tangential half-lightlike submanifold M of an indefinite Kenmotsu space form M-c,g- with semiparallel second fundamental form h either satisfies c=-1 or is J-RadTM,TM-mixed geodesic.

NON-EXISTENCE OF TOTALLY GEODESIC SCREEN DISTRIBUTIONS ON LIGHTLIKE HYPERSURFACES OF INDEFINITE KENMOTSU MANIFOLDS

We study lightlike hypersurfaces of indefinite Kenmotsu manifolds. The purpose of this paper is to prove that there do not exist totally geodesic screen distributions on semi-symmetric lightlike hypersurfaces of indefinite Kenmotsu manifolds with flat transversal connection.

Geodesic Lightlike Submanifolds of Indefinite Kenmotsu Manifolds

The aim of the present paper is to study geodesic contact screen Cauchy Riemannian (SCR-) lightlike submanifolds, geodesic screen transversal lightlike, and geodesic transversal lightlike submanifolds of indefinite Kenmotsu manifolds.

Hemi-Slant Lightlike Submanifolds of Indefinite Kenmotsu Manifolds

We introduce and study hemi-slant lightlike submanifolds of an indefinite Kenmotsu manifold. We give an example of hemi-slant lightlike submanifold and establish two characterization theorems for the existence of such submanifolds. We prove some theorems which ensure the existence of minimal hemi-slant lightlike submanifolds and obtain a condition under which the induced connection ∇ on M is a metric connection. An example of proper minimal hemi-slant lightlike submanifolds is also given.

LOCALLY SYMMETRIC HALF LIGHTLIKE SUBMANIFOLDS IN AN INDEFINITE KENMOTSU MANIFOLD

In this paper, we study locally symmetric half lightlike submanifolds M of an indefinite Kenmotsu manifold <TEX>$\bar{M}$</TEX> subject to the conditions: (1) The transversal vector bundle <TEX>$tr(TM)$</TEX> is parallel with respect to the connection <TEX>$\bar{\nabla}$</TEX> of <TEX>$\bar{M}$</TEX> and (2) M is irrotational.

Symmetries of Null Geometry in Indefinite Kenmotsu Manifolds

Null hypersurfaces have metrics with vanishing determinants and this degeneracy of these metrics leads to several difficulties. In this paper, null hypersurfaces of indefinite Kenmotsu space forms, tangent to the structure vector field, are studied with specific attention to locally symmetric, semi-symmetric and Ricci semi-symmetric null hypersurfaces. We show that locally symmetric and semi-symmetric null hypersurfaces are totally geodesic and parallel. These also hold for Ricci semi-symmetric null hypersurfaces, under a certain condition. We prove that, in null Einstein hypersurfaces of an indefinite Kenmotsu space form, tangent to the structure vector field, the local symmetry, semisymmetry and Ricci semi-symmetry notions are equivalent. For totally contact umbilical null hypersurfaces, we show that there are η-“Weyl” connections adapted to the induced structure on the null hypersurface.

On lightlike geometry in indefinite Kenmotsu manifolds

Abstract We investigate some geometric aspects of lightlike hypersurfaces of indefinite Kenmotsu manifolds, tangent to the structure vector field, by paying attention to the geometry of leaves of integrable distributions. Theorems on parallel vector fields, Killing distribution, geodesibility of their leaves are obtained. The geometric configuration of such lightlike hypersurfaces and leaves of its screen integrable distributions are established. We show that no totally contact umbilical leaf of a screen integrable distribution of a lightlike hypersurface can be an extrinsic sphere. We also prove that the geometry of any leaf of an integrable distribution is closely related to the geometry of a normal bundle.

Lightlike Geometry of Leaves in Indefinite Kenmotsu Manifolds

En este trabajo se estudian algunos aspectos de la geometria de las hojas de distribuciones integrables de las hipersuperficies luminosas en variedades de Kenmotsu indefinidas, tangentes a la estructura de un campo vectorial. Se obtienen algunos teoremas sobre el campo de vectores paralelo, distribucion de Killing y geodesbilidad de hipersuperficies liminosas. Se dan algunos teoremas de caracterizacion de las hojas de las distribuciones integrables. Se demuestra que existe una distribucion, subconjunto de la distribucion de la pantalla, en la que, bajo la condicion de integrabilidad, cualquier contacto con la hoja umbilical es una esfera extronseca.