in this paper, the lorentzian version of beltrami-euler formula is investigated in 1n . initially,the first fundamental form and the metric coefficients of generalized timelike ruled surface are calculated and by the help of the christoffel symbols, riemann-christoffel curvatures are obtained. thus, the curvatures of spacelike and timelike tangential sections of generalized timelike ruled surf...

We prove the non-existence of Levi flat compact real hypersurfaces without boundary in CPn, n > 1, with non-negative totally real Ricci curvature.

We obtain a basic inequality involving the Laplacian of the warping function and the squared mean curvature of any warped product isometrically immersed in a Riemannian manifold (cf. Theorem 2.2). Applying this general theory, we obtain basic inequalities involving the Laplacian of the warping function and the squared mean curvature of C-totally real warped product submanifolds of (κ, μ)-space ...

hadamard (or complete $cat(0)$) spaces are complete, non-positive curvature, metric spaces. here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. our results extend the standard non-linear ergodic theorems for non-expansive maps on real hilbert spaces, to non-expansive maps on had...

Let Mn be a Riemannian n-manifold. Denote by S(p) and Ric(p) the Ricci tensor and the maximum Ricci curvature on Mn, respectively. In this paper we prove that every C-totally real submanifolds of a Sasakian space form M̄2m+1(c) satisfies S ≤ ( (n−1)(c+3) 4 + n 2 4 H2)g, where H2 and g are the square mean curvature function and metric tensor on Mn, respectively. The equality holds identically if ...

Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...

Let N be the class of closed simply connected, smooth n–manifolds that admit nonnegative sectional curvature and let P be the corresponding class for positive curvature. Known examples suggest that N ought to be much larger than P . On the other hand, there is no known obstruction that distinguishes between the two classes. So its actually possible that N = P . In [PetWilh2] we will give a defo...