ON CONTACT METRIC HYPERSURFACES IN A REAL SPACE FORM
SCIE
SCOPUS
- Title
- ON CONTACT METRIC HYPERSURFACES IN A REAL SPACE FORM
- Authors
- Ozgur, C; Tripathi, MM; Hong, S
- Date Issued
- 2007-12
- Publisher
- ACADEMIC PUBLICATION COUNCIL
- Abstract
- For a (2n + 1)-dimensional N(k)-contact metric hypersurface in a real space form (M) over tilde (c), some main results are obtained as follows: (1) if k - c > 0 then M is totally umbilical, and consequently, either M is a Sasakian manifold of constant curvature +1 or M is 3-dimensional and flat; (2) if k = c and M is Einstein then either M is totally geodesic or a developable hypersurface in (M) over tilde (k), in particular M is of constant curvature and consequently, either M is a Sasakian manifold of constant curvature +1 or M is 3-dimensional and flat; (3) if M is 3-dimensional non-Sasakian such that k = c then either M is flat or the shape operator of M is of a specific form (see Theorem 6); and (4) if M is eta-Einstein such that n >= 2 and k = c, then M is a developable hypersurface. An obstruction for M to be totally geodesic is also obtained.
- Keywords
- (k, mu)-manifold; N(k)-contact metric manifold; N(k)-contact metric hypersurface; developable hypersurface; Einstein manifold; eta-Einstein manifold; CURVATURE
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/29503
- ISSN
- 1024-8684
- Article Type
- Article
- Citation
- KUWAIT JOURNAL OF SCIENCE & ENGINEERING, vol. 34, no. 2A, page. 25 - 40, 2007-12
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