Abstract
In this study, the coefficients of the p-fundamental forms of a hypersurface N imbedded in n-dimensional Riemannian space M were expressed in terms of the coefficients of first and se- cond fundamental forms. Then, by means of Cayley-Hamilton theorem, the inverse S-1 of the shape operatör S on the hypersurface N was vvritten as the combinations of the powers of S and the curvatures K n ... K p Thus the new fundamental forms and some properties of them cal- led the inverse fundamental forms, were defined and investigated. As a result of an application of the generalized divergence theorem of Gauss to the divergence relations of certain tensor fi- elds över the region R of N that can be expressed in terms of polynomials involving the new de fined curvatures of M an integral formula was obtained.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
