[Hypersurfaces of a Riemannian vector bundle with prescribed Gaussian curvature]
Let M be a compact Riemannian manifold, E a Riemannian vector bundle on M and Σ the sphere subbundle of E. We look for embeddings of Σ into E admitting prescribed Gaussian curvatures of various types.
Soient M une variété Riemannienne compacte, E un fibré vectoriel Riemannien sur M et Σ le sous-fibré unitaire de E. On détermine des plongements de Σ dans E dont on prescrit des courbures de Gauss de divers types.
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Abdellah Hanani 1
@article{CRMATH_2002__335_11_927_0, author = {Abdellah Hanani}, title = {Hypersurfaces d'un fibr\'e vectoriel {Riemannien} \`a courbure de {Gauss} prescrite}, journal = {Comptes Rendus. Math\'ematique}, pages = {927--930}, publisher = {Elsevier}, volume = {335}, number = {11}, year = {2002}, doi = {10.1016/S1631-073X(02)02588-8}, language = {fr}, }
Abdellah Hanani. Hypersurfaces d'un fibré vectoriel Riemannien à courbure de Gauss prescrite. Comptes Rendus. Mathématique, Volume 335 (2002) no. 11, pp. 927-930. doi : 10.1016/S1631-073X(02)02588-8. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02588-8/
[1] Nonlinear second order elliptic equations IV. Starshaped compact Weingarten hypersurfaces (Y. Ohya; K. Kasahara; N. Shimakura, eds.), Current Topics in Partial Differential Equations, Kinokunize, Tokyo, 1986, pp. 1-26
[2] Plongements radiaux à courbure de Gauss positive prescrite, Ann. Sci. École Norm. Sup., Volume 18 (1985), pp. 635-649
[3] Local inversion of elliptic problems on compact manifolds, Math. Japon., Volume 35 (1990), pp. 679-692
[4] The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc., Volume 7 (1982), pp. 65-222
[5] Degree of mapping in convex linear topological spaces, Amer. J. Math., Volume 73 (1951), pp. 497-511
[6] Hypersurfaces in with prescribed Gaussian curvature and related equations of Monge–Ampère type, Comm. Partial Differential Equations, Volume 9 (1984), pp. 807-838
[7] Tangent and Cotangent Bundles, Marcel Dekker, New York, 1973
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