On generic submanifolds of a locally conformal Kähler manifold with parallel canonical structures.
We will prove that if an open subset of is isometrically immersed into , with , then the image is totally geodesic. We will also prove that if an open subset of isometrically immersed into , with , then the image is totally geodesic.
We give a pinching theorem for a compact minimal generic submanifold with flat normal connection immersed in an odd-dimensional sphere with standard Sasakian structure.
Elastica and inextensible flows of curves play an important role in practical applications. In this paper, we construct a new characterization of inextensible flows by using elastica in space. The inextensible flow is completely determined for any space-like curve in de Sitter space [...] S 1 3 . Finally, we give some characterizations for curvatures of a space-like curve in de Sitter space [...] S 1 3 .
Many authors have studied the geometry of submanifolds of Kaehlerian and Sasakian manifolds. On the other hand, David E. Blair has initiated the study of S-manifolds, which reduce, in particular cases, to Sasakian manifolds ([1, 2]). I. Mihai ([8]) and L. Ornea ([9]) have investigated CR-submanifolds of S-manifolds. The purpose of the present paper is to study a special kind of such submanifolds, namely the normal CR-submanifolds. In Sections 1 and 2, we review basic formulas and definitions for...