We prove some pinching theorems with respect to the scalar curvature of 4-dimensional conformally flat (concircularly flat, quasi-conformally flat) totally real minimal submanifolds in QP⁴(c).
In this paper, we prove a theorem for -dimensional totally real minimal submanifold immersed in quaternion space form.
2000 Mathematics Subject Classification: 53C40, 53B25.In the present note we study totally umbilical pseudo-slant submanifolds of a nearly cosymplectic manifold. We have obtained a classification theorem for totally umbilical pseudo-slant submanifolds of a nearly cosymplectic manifold.
We introduce the notions of (extrinsic) locally transversally symmetric immersions and submanifolds in a Riemannian manifold equipped with a unit Killing vector field as analogues of those of (extrinsic) locally symmetric immersions and submanifolds. We treat their geometric properties, derive several characterizations and give a list of examples.