It is well known that the sphere $S^6(1)$ admits an almost complex structure $J$ which nearly K\"{a}hler. A submanifold $M$ of Hermitian manifold called a CR if it differentiable distribution $\mathcal{D}_1$ such its orthogonal complement totally real distribution. In this case normal bundle also splits into two distributions $\mathcal{D}_3$, complex, and complement. proper three-dimensional si...

in this paper we study isotropic lagrangian submanifolds , in complex space forms . it is shown that they are either totally geodesic or minimal in the complex projective space , if . when , they are either totally geodesic or minimal in . we also give a classification of semi-parallel lagrangian h-umbilical submanifolds.

In this paper, we study submanifolds in a Riemannian manifold with a semi-symmetric non-metric connection. We prove that the induced connection on a submanifold is also semi-symmetric non-metric connection. We consider the total geodesicness and minimality of a submanifold with respect to the semi-symmetric non-metric connection. We obtain the Gauss, Cadazzi, and Ricci equations for submanifold...

We prove a converse to well-known results by E. Cartan and J. D. Moore. Let f:Mcn?Qc˜n+p be an isometric immersion of Riemannian manifold with constant sectional curvature c into space form c˜, free weak-umbilic points if c>c˜. show that the substantial codimension f is p=n?1 if, as shown Moore, first normal bundle possesses lowest possible rank n?1. These submanifolds are class has been extens...

By using two new algebraic lemmas we obtain Chen’s inequalities for submanifolds of a Riemannian manifold of nearly quasi-constant curvature endowed with a semi-symmetric non-metric connection. Moreover, we correct a result of C. Özgür and A. Mihai’s paper (Chen inequalities for submanifolds of real space forms with a semi-symmetric non-metric connection, Canad. Math. Bull. 55 (2012), 611–622).

Warped product manifolds provide excellent setting to model space-time near black holes or bodies with large gravitational force (cf. [1], [2], [14]). Recently, results are published exploring the existence (or non-existence) of warped product submanifolds in Kaehlerian and contact settings (cf. [6], [17], [20]). To continue the sequel, we have considered warped product submanifolds of nearly K...

Abstract: In this paper, we prove some optimal inequalities involving the intrinsic scalar curvature and the extrinsic Casorati curvature of submanifolds in a generalized complex space form with a semi-symmetric non-metric connection and a generalized Sasakian space form with a semi-symmetric non-metric connection. Moreover, we show that in both cases, the equalities hold if and only if submani...

Submanifolds of Frobenius manifolds are studied. In particular, so-called natural submanifolds are defined and, for semi-simple Frobenius manifolds, classified. These carry the structure of a Frobenius algebra on each tangent space, but will, in general, be curved. The induced curvature is studied, a main result being that these natural submanifolds carry a induced pencil of compatible metrics....

We introduce the geometry of pseudo-totally umbilical lightlike submanifold $M$ a semi-Riemannian manifold $\bar{M}$. In line with above, we give complete classification $1$-lightlike submanifolds, such as hypersurfaces and half-lightlike submanifolds. Furthermore, screen distributions are also investigated, for any whose umbilical. Closely linked to above show, under some geometric conditions,...

In this paper, we study half-lightlike submanifolds of a semi-Riemannian manifold such that the shape operator of screen distribution is conformal to the shape operator of screen transversal distribution. We mainly obtain some results concerning the induced Ricci curvature tensor and the null sectional curvature of screen transversal conformal half-lightlike submanifolds. 2010 Mathematics Subje...