SECTIONAL CURVATURES OF GRASSMANN MANIFOLDS

On Sectional Curvatures of (ε)-Sasakian Manifolds

The index of a metric plays significant roles in differential geometry as it generates variety of vector fields such as space-like, time-like, and light-like fileds. With the help of these vector fields, we establish interesting properties on ( )-Sasakian manifolds, which was introduced by Bejancu and Duggal [1] and further investigated by Xufeng and Xiaoli [2]. Since Sasakian manifolds with in...

Totally umbilical radical transversal lightlike hypersurfaces of Kähler-Norden manifolds of constant totally real sectional curvatures

In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahler-Norden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$...

Hermitian Manifolds of Pointwise Constant Antiholomorphic Sectional Curvatures

In dimension greater than four, we prove that if a Hermitian non-Kaehler manifold is of pointwise constant antiholomorphic sectional curvatures, then it is of constant sectional curvatures.

Space Forms of Grassmann Manifolds

Cobordism independence of Grassmann manifolds

This paper is a continuation of the ongoing study of cobordism of Grassmann manifolds. Let F denote one of the division rings R of reals, C of complex numbers, or H of quaternions. Let t = dimRF . Then the Grassmannian manifold Gk(F) is defined to be the set of all k-dimensional (left) subspaces of Fn+k. Gk(F) is a closed manifold of real dimension nkt. Using the orthogonal complement of a subs...