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  • 1
    Electronic Resource
    Electronic Resource
    The third fundamental form metric for hypersurfaces in nonflat space forms (1999)
    Springer
    Journal of geometry 65 (1999), S. 130-142 
    Details
    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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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Codazzi Tensors and the Topology of Surfaces (1998)
    Springer
    Annals of global analysis and geometry 16 (1998), S. 189-202 
    Details
    ISSN: 1572-9060
    Keywords: Codazzi tensor ; index method ; topologyof surfaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We introduce the notion of (0,m)-Codazzi tensors relative to an affine connection which extends the well known concept for m = 2. On compact Riemannian surfaces of genus γ we determine the dimension of the R-vector space of traceless Codazzi tensors, which depends on m and γ only, additionally we extend these result for genus zero. We give some exemplary applications to submanifolds in affine and in Riemannian geometry and to Weyl geometries.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006582620941
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    Paper (German National Licenses)
    Fulltext
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