International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 9, Pages 539-547
A basic inequality for submanifolds in a cosymplectic space form
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
Copyright © 2003 Jeong-Sik Kim and Jaedong Choi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 and the squared mean curvature,
are given. The equality cases are also discussed.