We obtain the expressions for sectional curvature, holomorphic sectional curvature, and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite Kaehler manifold. We discuss the boundedness of holomorphic sectional curvature of GCR-lightlike submanifolds of an indefinite complex space form. We establish a condition for a GCR-lightlike submanifold of an indefinite comple...

Given a Riemannian manifold together with a group of isometries, we discuss MCF of the orbits and some applications: eg, finding minimal orbits. We then specialize to Lagrangian orbits in Kaehler manifolds. In particular, in the Kaehler-Einstein case we find a relation between MCF and moment maps which, for example, proves that the minimal Lagrangian orbits are isolated.

I Berger, M., "Sur quelques varigtes riemanniennes compactes d'Einstein," Compt. Rend., 260, 1554-1557 (1965). 2 Bishop, R. L., and R. J. Crittenden, Geometry of Manifolds (New York: Academic Press, 1964). 3Bishop, R. L., and S. I. Goldberg, "On the topology of positively curved Kaehler manifolds," T6hoku Math. J., 15, 359-364 (1963). 4 Bishop, R. L., and S. I. Goldberg, "On the second cohomolo...

‎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.

Cosymplectic manifolds provide a natural setting for time dependent mechanical systems as they are locally product of a Kaehler manifold and a one dimensional manifold. Thus study of warped product submanifolds of cosymplectic manifolds is significant. In this paper we have proved results on the non-existence of warped product submanifolds of certain types in cosymplectic manifolds. M.S.C. 2000...

In the present note we study the existence or non-existence of doubly warped and doubly twisted product CR-submanifolds in nearly Kaehler manifolds.

Recently, Sahin [10] studied the anti-invariant Riemannian submersions from almost Hermitian manifolds onto manifolds. In present work, these notions of and Lagrangian have been extended to locally conformal Kaehler Certain decomposition results geometry foliation also investigated.