Codazzi-Tensoren und Kennzeichnungen sphärischer Immersionen

Wegner, Bernd

doi:10.4310/jdg/1214432091

Cited by 22 publications

(8 citation statements)

References 9 publications

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“…Similar theorems have been proved by a different method by Berger and Ebin [2], Ryan [18], Simon [20], [21] and Wegner [24], [25]. Similar theorems have been proved by a different method by Berger and Ebin [2], Ryan [18], Simon [20], [21] and Wegner [24], [25].…”

Section: Introductionmentioning

confidence: 58%

Einstein-like manifolds which are not Einstein

1978

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Section: Introductionmentioning

confidence: 58%

Einstein-like manifolds which are not Einstein

1978

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“…also [19]), is the main step for proving our Theorem 1. It reduces all the arguments involving differentiations of a given Codazzi tensor to the mere fact that the curvature tensor of some new Riemannian metric has the generally valid symmetries, which makes the proof of Theorem 1 purely algebraic.…”

Section: Consequences For the Curvaturementioning

confidence: 99%

Codazzi Tensor Fields, Curvature and Pontryagin Forms

Derdziński

Chen

1983

Proceedings of the London Mathematical Society

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“…For (iv): For every parallel normal vector field ¢ (over U) the Bochner formula for the Laplacian of II A¢II 2 (see [35,Satz 1]) yields 0= ~ mims(~+<r/i,r/j))<r/i--r/j,~>2+ IIV*A¢IL 2.…”

Section: Theorem 2 Suppose That F: M ~ )Fl(c') Is An Isoparametric Imentioning

confidence: 99%

Isoparametric submanifolds

Str�bing

1986

Geom Dedicata

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We consider isometric immersions F: M --* h4 between Riemannian manifolds whose higher mean curvature forms [in the sense of the author, Manuscripta Math. 49 (1984), 177-194] are all (covariantly) constant or, equivalently, whose shape operator with respect to each parallel unit normal vector field along any curve in M has constant eigenvalues: As in the hypersurface case we call such immersions isoparametric. Among other results it is proved: Isoparametric surfaces of constant curvature spaces are symmetric, i.e. have parallel second fundamental form. The same is true for isoparametric K/ihlerian hypersurfaces of complex space forms. AMS (MOS) SUBJECT CLASSIFICATIONS: (1980): 53B25, 53A07, 53C42 KEY WORDS: higher mean curvature forms, isoparametric, symmetric submanifolds Geometriae Dedicata 211 (1986), 367-387.

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Codazzi-Tensoren und Kennzeichnungen sphärischer Immersionen

Cited by 22 publications

References 9 publications

Einstein-like manifolds which are not Einstein

Einstein-like manifolds which are not Einstein

Codazzi Tensor Fields, Curvature and Pontryagin Forms

Isoparametric submanifolds

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