International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 9, Pages 539-547
doi:10.1155/S0161171203202027

A basic inequality for submanifolds in a cosymplectic space form

Jeong-Sik Kim1 and Jaedong Choi2

 1Department of Mathematics Education, Sunchon National University, Sunchon 540-742, Korea
2Department of Mathematics, P.O. Box 335-2, Airforce Academy, Ssangsu, Namil, Chungwon, Chungbuk, 363-849, Korea
Received 7 February 2002

Abstract

For submanifolds tangent to the structure vector field in cosymplectic space forms, we establish a basic inequality between the main intrinsic invariants of the submanifold, namely, its sectional curvature and scalar curvature on one side; and its main extrinsic invariant, namely, squared mean curvature on the other side. Some applications, including inequalities between the intrinsic invariant δM and the squared mean curvature, are given. The equality cases are also discussed.