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The third fundamental form metric for hypersurfaces in nonflat space forms (1999)

Liu, H. L. ; Simon, U. ; Verstraelen, L. ; [et al.]

Springer

Journal of geometry 65 (1999), S. 130-142

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ISSN: 1420-8997

Keywords: 53 B 25 ; 53 C 42 ; 53 C 25 ; third fundamental form metric ; hypersurfaces in nonflat space forms ; Einstein metric ; Codazzi tensor ; isoparametric hypersurfaces

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract For hypersurfaces with regular Weingarten operator in nonflat space forms we study the relations between the intrinsic geometry of the third fundamental form metric and the extrinsic geometry of the hypersurface. We prove a theorema-egregium-type result for this metric and, in particular, give a local classification of hypersurfaces in case of an Einstein structure of this metric.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01228684

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