A conformal differential invariant and the conformal rigidity of hypersurfaces

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dc.creatorAkivis, Maks A.
dc.creatorGoldberg, Vladislav V.
dc.date1998-05-30
dc.date.accessioned2026-07-07T06:32:58Z
dc.date.available2026-07-07T06:32:58Z
dc.descriptionFor a hypersurface V of a conformal space, we introduce a conformal differential invariant I = h^2/g, where g and h are the first and the second fundamental forms of V connected by the apolarity condition. This invariant is called the conformal quadratic element of V. The solution of the problem of conformal rigidity is presented in the framework of conformal differential geometry and connected with the conformal quadratic element of V. The main theorem states: Let n \geq 4 and V and V' be two nonisotropic hypersurfaces without umbilical points in a conformal space C^n or a pseudoconformal space C^n_q of signature (p, q), p = n - q. Suppose that there is a one-to-one correspondence f: V ---> V' between points of these hypersurfaces, and in the corresponding points of V and V' the following condition holds: I' = f_* I, where f_*: T (V) ---> T (V) is a mapping induced by the correspondence f. Then the hypersurfaces V and V' are conformally equivalent.
dc.descriptionLaTeX, 10 pages
dc.identifierhttps://arxiv.org/abs/math/9806001
dc.identifierhttp://arxiv.org/abs/math/9806001
dc.identifierProc. Amer. Math. Soc. 125 (1997), no. 8, 2415-2424
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99039
dc.subjectDifferential Geometry
dc.subject53A30 (Primary), 53B25 (Secondary)
dc.titleA conformal differential invariant and the conformal rigidity of hypersurfaces
dc.typetext

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