‎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.

We study the Lie algebra of infinitesimal isometries on compact Sasakian and K–contact manifolds. On a Sasakian manifold which is not a space form or 3– Sasakian, every Killing vector field is an infinitesimal automorphism of the Sasakian structure. For a manifold with K–contact structure, we prove that there exists a Killing vector field of constant length which is not an infinitesimal automor...

in this paper, we give some characterizations for legendre spherical, legendre normal and legendre rectifying curves in the 3-dimensional sasakian space. furthermore, we show that legendre spherical curves are also legendre normal curves. in particular, we prove that the inverse of curvature of a legendre rectifying curve is a non-constant linear function of the arclength parameter.

In this paper we introduce the concept of (ε)-almost paracontact manifolds, and in particular, of (ε)-para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of (ε)-para Sasakian manifolds are obtained. We prove that if a semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it can not admit an (ε...

We study the Lie algebra of infinitesimal isometries of 7–dimensional simply connected manifolds with Killing spinors. We obtain some splitting theorems for the action of this algebra on the space of Killing spinors, and as a corollary we prove that there are no infinitesimal isometry of constant length on a 7–dimensional 3– Sasakian manifold (not isometric to a space form) except the linear co...

This review article has grown out of notes for the three lectures the second author presented during the XXIV-th Winter School of Geometry and Physics in Srni, Czech Republic, in January of 2004. Our purpose is twofold. We want give a brief introduction to some of the techniques we have developed over the last 5 years while, at the same time, we summarize all the known results. We do not give a...

We study the Lie algebra of innnitesimal isometries of 7{dimensional simply connected manifolds with Killing spinors. We obtain some splitting theorems for the action of this algebra on the space of Killing spinors, and as a corollary we prove that there are no innnites-imal isometry of constant length on a 7{dimensional 3{Sasakian manifold (not isometric to a space form) except the linear comb...

We discuss the Sasakian geometry of odd dimensional homotopy spheres. In particular, we give a completely new proof of the existence of metrics of positive Ricci curvature on exotic spheres that can be realized as the boundary of a parallelizable manifold. Furthermore, it is shown that on such homotopy spheres Σ the moduli space of Sasakian structures has infinitely many positive components det...

In this paper, we study half lightlike submanifolds M of an indefinite generalized Sasakian space form M̄(f1, f2, f3), with an indefinite trans-Sasakian structure of type (α, β), subject to the condition that the structure vector field of M̄ is tangent to M . Our main result is a characterization theorem for such a half lightlike submanifold. Mathematics Subject Classification: 53C25, 53C40, 53C50

In this paper, we study the geometry of lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection. The main result is a characterization theorem for such a lightlike hypersurface of an indefinite generalized Sasakian space form. Mathematics Subject Classification: 53C25, 53C40, 53C50