A Basic Inequality for the Tanaka-Webster Connection. (18th January 2012)

• Record Type: Journal Article
• Authors: Jin, Dae Ho; Lee, Jae Won
• Other Names: Conca C. Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2012(2012)
• Publication Date: 2012-01-18
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2012/231416
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : For submanifolds tangent to the structure vector field in Sasakian space forms, we establish a Chen's basic inequality between the main intrinsic invariants of the submanifold (namely, its pseudosectional curvature and pseudosectional curvature on one side) and the main extrinsic invariant (namely, squared pseudomean curvature on the other side) with respect to the Tanaka-Webster connection. Moreover, involving the pseudo-Ricci curvature and the squared pseudo-mean curvature, we obtain a basic inequality for submanifolds of a Sasakian space form tangent to the structure vector field in terms of the Tanaka-Webster connection.