Anti-invariant Submanifolds Research Articles

Invariant and Anti-Invariant Submanifolds of Generalized Sasakian Space Forms

Invariant and Anti-Invariant Submanifolds of Generalized Sasakian Space Forms

Solitons of η-Ricci–Bourguignon Type on Submanifolds in (LCS)m Manifolds

In this research article, we concentrate on the exploration of submanifolds in an (LCS)m-manifold B˜. We examine these submanifolds in the context of two distinct vector fields, namely, the characteristic vector field and the concurrent vector field. Initially, we consider some classifications of η-Ricci–Bourguignon (in short, η-RB) solitons on both invariant and anti-invariant submanifolds of B˜ employing the characteristic vector field. We establish several significant findings through this process. Furthermore, we investigate additional results by using η-RB solitons on invariant submanifolds of B˜ with concurrent vector fields, and discuss a supporting example.

Generalized warped product submanifolds of Lorentzian concircular structure manifolds

<abstract><p>We began by considering invariant, anti-invariant, proper slant, and pointwise slant submanifolds of a Lorentzian concircular structure manifold. Subsequently, we explored two distinct categories of warped product submanifolds. The first category encompassed the fiber submanifold as an anti-invariant submanifold, while the second category included the fiber submanifold as a pointwise slant submanifold. We established several fundamental results concerning these submanifold classes. Additionally, we demonstrated the existence of such submanifold classes through specific examples. Moreover, we derived inequalities for the squared norm of the second fundamental form.</p></abstract>

Some Optimal Inequalities for Anti-invariant Submanifolds of the Unit Sphere

Some Optimal Inequalities for Anti-invariant Submanifolds of the Unit Sphere

The Stability Problem of Certain Anti-Invariant Submanifolds in Golden Riemannian Manifolds

In this study, we discuss the stability of some anti-invariant submanifolds of golden Riemannian manifolds under certain conditions in terms of the Ricci curvature tensors of the ambient manifold and the submanifold.

On anti-invariant submanifolds in Sasakian manifolds with vanishing contact Bochner curvature tensor

On anti-invariant submanifolds in Sasakian manifolds with vanishing contact Bochner curvature tensor

On submanifolds of Sasakian statistical manifolds

‎In this paper‎, ‎invariant and‎ ‎anti-invariant submanifolds of Sasakian statistical manifolds are studied‎. ‎Necessary and sufficient conditions are given for vanishing the dual connection in the normal bundle‎. ‎Moreover‎, ‎existence of a Kaehlerian structure on invariant hypersurfaces of Sasakian statistical manifolds are proved‎.

Anti-invariant submanifolds of a normal paracontact metric manifold

In this paper, anti-invariant submanifolds of a normal paracontact metric manifold are studied and characterizing the submanifold with respect to covariant derivative of the second fundamental form of anti-invariant submanifold. Furthermore, some special cases are also discussed and we give a non-trivial example which satisfies the statements of theorems.

Some characterizations of anti-invariant submanifolds of trans-sasakian manifolds

The object of this paper is to study anti-invariant submanifolds of trans-Sasakian manifolds. We characterize such submanifolds on the basis of parallelism, semi-parallelism and pseudo parallelism of the second fundamental form of the submanifolds. We also characterize totally umbilical anti-invariant submanifolds of trans-Sasakian manifolds. Existence of Legendre curves on such submanifolds has been analyzed. Whether an anti-invariant submanifold of a trans-Sasakian manifold inherits local symmetry from ambient space is investigated here. Nature of Ricci soliton on anti-invariant submanifolds of trans-Sasakian manifolds has been characterized.

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.

Inequalities for generalized normalized $$\delta $$-Casorati curvatures of slant submanifolds in metallic Riemannian space forms

In the present paper, we establish sharp inequalities involving generalized normalized $$\delta $$ -Casorati curvatures for invariant, anti-invariant and slant submanifolds in metallic Riemannian space forms and characterize the submanifolds for which the equality holds.

A class of warped product submanifolds of Kenmotsu manifolds

In 2018 Naghi et al. studied warped product skew CR-submanifold of the form M = M1×f M⊥ of a Kenmotsu manifold M¯ throughout the paper , where M1 = MT ×Mθ and MT , M⊥, Mθ represents invariant, antiinvariant, proper slant submanifold of M¯ . Next, in 2019 Hui et al. studied another class of warped product skew CR-submanifold of the form M = M2 ×f MT of M¯ , where M2 = M⊥ × Mθ . The present paper deals with the study of a class of warped product submanifold of the form M = M3 ×f Mθ of M¯ , where M3 = MT × M⊥ and MT , M⊥, Mθ represents invariant, antiinvariant and proper pointwise slant submanifold of M¯ . A characterization is given on the existence of such warped product submanifolds which generalizes the characterization of warped product contact CR-submanifolds of the form M⊥ ×f MT , studied by Uddin et al. in 2017 and also generalizes the characterization of warped product semi-slant submanifolds of the form MT ×f Mθ , studied by Uddin in the same year. Beside that some inequalities on the squared norm of the second fundamental form are obtained which are also generalizations of the inequalities obtained in the just above two mentioned papers respectively.

Submanifolds of almost poly-Norden Riemannian manifolds

Our aim in the present paper is to initiate the study of submanifolds in an almost poly-Norden Riemannian manifold, which is a new type of manifold first introduced by Sahin [17]. We give fundamental properties of submanifolds equipped with induced structures provided by almost poly-Norden Riemannian structures and find some conditions for such submanifolds to be totally geodesics. We introduce some subclasses of submanifolds in almost poly-Norden Riemannian manifolds such as invariant and antiinvariant submanifolds. We investigate conditions for a hypersurface of almost poly-Norden Riemannian manifolds to be invariant and totally geodesic, respectively, by using the components of the structure induced by the almost poly-Norden Riemannian structure of the ambient manifold. We also obtain some characterizations for totally umbilical hypersurfaces and give some examples of invariant and noninvariant hypersurfaces.

Submanifolds in Normal Complex Contact Manifolds

In the present article we initiate the study of submanifolds in normal complex contact metric manifolds. We define invariant and anti-invariant ( C C -totally real) submanifolds in such manifolds and start the study of their basic properties. Also, we establish the Chen first inequality and Chen inequality for the invariant δ ( 2 , 2 ) for C C -totally real submanifolds in a normal complex contact space form and characterize the equality cases. We also prove the minimality of C C -totally real submanifolds of maximum dimension satisfying the equalities.

Submanifolds with parallel mean curvature vector in η-Einstein Sasaki manifold

In this note, we prove that for a 3-dimensional submanifold in an η-Einstein 5-Sasaki manifold with Einstein constant a≥4, if the Reeb vector field is tangent to the submanifold and it has parallel mean curvature form, then it is a slant submanifold. Furthermore, if a>4, then it is either an invariant submanifold or an anti-invariant submanifold.

In this paper, we present some mathematical mistakes of the paper titled "On ¯G ?J anti-invariant submanifolds of almost complex contact metric manifolds, New Trends in Mathematical Sciences, NTMSCI 4, No. 3, 277-289 (2016)."

In this paper, we present some mathematical mistakes of the paper titled "On ¯G ?J anti-invariant submanifolds of almost complex contact metric manifolds, New Trends in Mathematical Sciences, NTMSCI 4, No. 3, 277-289 (2016)."

Some Results on Anti-Invariant Submanifolds of \((LCS)_N\)-Manifold

The object of the present paper is to study anti-invariant submanifolds \(M\) of \((LCS)_{n}\)-manifold \(\bar{M}\). The basic equations are decomposed into horizontal and vertical homomorphisms and geometric properties of anti-invariant submanifolds are studied.

Inequalities for submanifolds of Sasaki-like statistical manifolds

We consider statistical submanifolds in Sasaki-like statistical manifolds. We give some examples of invariant and antiinvariant submanifolds of Sasaki-like statistical manifolds. We prove Chen-like inequality involving scalar curvature and Chen-Ricci inequality for these kinds of submanifolds.

Invariant and anti-invariant submanifolds of special quasi-sasakian manifolds

The present paper deals with the study of Chaki-pseudo parallel and Deszcz-pseudo parallel invariant submanifolds of SQ-Sasakian manifolds with respect to Levi–Civita connection as well as semisymmetric metric connection. It is obtained that these two classes are equivalent with a certain condition. In addition, invariant and anti-invariant submanifolds of SQ-Sasakian manifolds with respect to Levi–Civita connection as well as semisymmetric metric connection whose metrics are Ricci solitons are studied.

Lower extremities for generalized normalized δ-Casorati curvatures of bi-slant submanifolds in generalized complex space forms

In this paper, we obtain the inequalities for the generalized normalized δ-Casorati curvature and the normalized scalar curvature for different submanifolds in generalized complex space form, which is based on an optimization procedure involving a quadratic polynomial in the components of the second fundamental form and characterizes the submanifolds on which equalities hold. We also develop, the same inequalities for semi-slant, hemi-slant, CR, slant, invariant and anti-invariant submanifolds in the same target space and consider the equality case. Moreover, we obtain a geometric inequality involving Casorati curvature for warped product bi-slant submanifolds in same ambient and obtain an obstruction result.