‎we prove that there do not exist totally contact umbilical‎ ‎proper slant lightlike submanifolds of indefinite sasakian manifolds other than totally contact geodesic‎ ‎proper slant lightlike submanifolds‎. ‎we also prove that there do‎ ‎not exist totally contact umbilical proper slant lightlike‎ ‎submanifolds of indefinite sasakian space forms‎.

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.

‎We prove that there do not exist totally contact umbilical‎ ‎proper slant lightlike submanifolds of indefinite Sasakian manifolds other than totally contact geodesic‎ ‎proper slant lightlike submanifolds‎. ‎We also prove that there do‎ ‎not exist totally contact umbilical proper slant lightlike‎ ‎submanifolds of indefinite Sasakian space forms‎.

In this paper, we study radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds giving some non-trivial examples of these submanifolds. Integrability conditions of distributions D and RadTM on radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite pa...

we study the notion of harmonicity in the sense of symplectic geometry, and investigate the geometric properties of harmonic thom forms and distributional thom currents, dual to different types of submanifolds. we show that the harmonic thom form associated to a symplectic submanifold is nowhere vanishing. we also construct symplectic smoothing operators which preserve the harmonicity of distri...

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...

2 Contact manifolds 4 2.1 Contact manifolds and their submanifolds . . . . . . . . . . . . . . 6 2.2 Gray stability and the Moser trick . . . . . . . . . . . . . . . . . . 13 2.3 Contact Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Darboux’s theorem and neighbourhood theorems . . . . . . . . . . 17 2.4.1 Darboux’s theorem . . . . . . . . . . . . . . . . . . . . . . . 17...

Involving the Ricci curvature and the squared mean curvature, we obtain basic inequalities for different kind of submaniforlds of a Sasakian space form tangent to the structure vector field of the ambient manifold. Contrary to already known results, we find a different necessary and sufficient condition for the equality for Ricci curvature of C-totally real submanifolds of a Sasakian space form...

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.