Matches in SemOpenAlex for { <https://semopenalex.org/work/W2095428765> ?p ?o ?g. }
Showing items 1 to 78 of
78
with 100 items per page.
- W2095428765 abstract "In this paper the author proves some pinching theorems of Simons type for complete minimal submanifolds in the sphere, which generalize the relative results by Simons and Yau. In this paper we first prove a pinching theorem for complete minimal submanifolds in the sphere, which has been proved by J. Simons [4] in the compact case. Namely, if Mn is a complete submanifold in the sphere Sn 'P, and if the square of the length of the second fundamental form of Mn is not greater than n/(2 -lp), then Mn is totally geodesic. When p = 1, this theorem has been proved by T. Hasanis [2]. Furthermore, it turns out that many pinching theorems in Yau's paper [5] can be proved to be still true for the complete case in the same way. 1. Local formulas and basic lemmas. Let Mn be an n-dimensional manifold in the Euclidian unit sphere Snlp. We choose a local field of orthonormal frames e1,. . . ,e,... en+p in Sn+p such that, restricted to Mn, the vectors e ,..., en are tangent to Mn. Let w1,. . . , wn be the field of dual frames. We shall make use of the following convention on the ranges of indices: 1 < i, j, k,... < n, n + 1 < a, /3, y,... < n + p; we shall agree that repeated indices are summed over the respective ranges. We denote the second fundamental form of Mn by Ea jhwlwjea. The square of the length of the second fundamental form is defined by S = Za i j(h(' )2. We call H = (1/n)(Za ih )ea the mean curvature vector. Mn is said to be a minimal submanifold if H = 0 and a submanifold with parallel mean curvature if the normalized mean curvature vector is parallel in the normal bundle of Mn. The following equality is well known: (1) Rijkl = ( ik J/Si/S k) + Z(hakha hahak), a where Rijkl are the components of the curvature tensor of Mn. The following two lemmas are basic for our aim. Received by the editors June 26, 1984. 1980 Mathematics Subject Classification. Primary 53C40; Secondary 53C20. ' The author was supported by the Max-Planck-Institut fur Mathematik, Sonderforschungsbereich 40 of the University of Bonn. (?1985 American Mathematical Society 0002-9939/85 $1.00 + $.25 per page" @default.
- W2095428765 created "2016-06-24" @default.
- W2095428765 creator A5039838264 @default.
- W2095428765 date "1985-04-01" @default.
- W2095428765 modified "2023-09-26" @default.
- W2095428765 title "Pinching theorems of Simons type for complete minimal submanifolds in the sphere" @default.
- W2095428765 cites W2004498216 @default.
- W2095428765 cites W2078209456 @default.
- W2095428765 cites W2125507914 @default.
- W2095428765 cites W2322146979 @default.
- W2095428765 cites W377433279 @default.
- W2095428765 doi "https://doi.org/10.1090/s0002-9939-1985-0776208-4" @default.
- W2095428765 hasPublicationYear "1985" @default.
- W2095428765 type Work @default.
- W2095428765 sameAs 2095428765 @default.
- W2095428765 citedByCount "2" @default.
- W2095428765 crossrefType "journal-article" @default.
- W2095428765 hasAuthorship W2095428765A5039838264 @default.
- W2095428765 hasBestOaLocation W20954287651 @default.
- W2095428765 hasConcept C114614502 @default.
- W2095428765 hasConcept C119830904 @default.
- W2095428765 hasConcept C134306372 @default.
- W2095428765 hasConcept C135692309 @default.
- W2095428765 hasConcept C151300846 @default.
- W2095428765 hasConcept C165818556 @default.
- W2095428765 hasConcept C175017881 @default.
- W2095428765 hasConcept C18903297 @default.
- W2095428765 hasConcept C191948623 @default.
- W2095428765 hasConcept C195065555 @default.
- W2095428765 hasConcept C202444582 @default.
- W2095428765 hasConcept C2524010 @default.
- W2095428765 hasConcept C2777299769 @default.
- W2095428765 hasConcept C33923547 @default.
- W2095428765 hasConcept C86803240 @default.
- W2095428765 hasConcept C9652623 @default.
- W2095428765 hasConceptScore W2095428765C114614502 @default.
- W2095428765 hasConceptScore W2095428765C119830904 @default.
- W2095428765 hasConceptScore W2095428765C134306372 @default.
- W2095428765 hasConceptScore W2095428765C135692309 @default.
- W2095428765 hasConceptScore W2095428765C151300846 @default.
- W2095428765 hasConceptScore W2095428765C165818556 @default.
- W2095428765 hasConceptScore W2095428765C175017881 @default.
- W2095428765 hasConceptScore W2095428765C18903297 @default.
- W2095428765 hasConceptScore W2095428765C191948623 @default.
- W2095428765 hasConceptScore W2095428765C195065555 @default.
- W2095428765 hasConceptScore W2095428765C202444582 @default.
- W2095428765 hasConceptScore W2095428765C2524010 @default.
- W2095428765 hasConceptScore W2095428765C2777299769 @default.
- W2095428765 hasConceptScore W2095428765C33923547 @default.
- W2095428765 hasConceptScore W2095428765C86803240 @default.
- W2095428765 hasConceptScore W2095428765C9652623 @default.
- W2095428765 hasLocation W20954287651 @default.
- W2095428765 hasOpenAccess W2095428765 @default.
- W2095428765 hasPrimaryLocation W20954287651 @default.
- W2095428765 hasRelatedWork W1035948334 @default.
- W2095428765 hasRelatedWork W1663375000 @default.
- W2095428765 hasRelatedWork W1973498303 @default.
- W2095428765 hasRelatedWork W1973564825 @default.
- W2095428765 hasRelatedWork W1978862982 @default.
- W2095428765 hasRelatedWork W2009342913 @default.
- W2095428765 hasRelatedWork W2026052141 @default.
- W2095428765 hasRelatedWork W2026271349 @default.
- W2095428765 hasRelatedWork W2068603014 @default.
- W2095428765 hasRelatedWork W2071906275 @default.
- W2095428765 hasRelatedWork W2082531076 @default.
- W2095428765 hasRelatedWork W2136867814 @default.
- W2095428765 hasRelatedWork W2269470291 @default.
- W2095428765 hasRelatedWork W2348813941 @default.
- W2095428765 hasRelatedWork W2350032426 @default.
- W2095428765 hasRelatedWork W2356258394 @default.
- W2095428765 hasRelatedWork W2362927431 @default.
- W2095428765 hasRelatedWork W2384454119 @default.
- W2095428765 hasRelatedWork W2509591041 @default.
- W2095428765 hasRelatedWork W2580703331 @default.
- W2095428765 isParatext "false" @default.
- W2095428765 isRetracted "false" @default.
- W2095428765 magId "2095428765" @default.
- W2095428765 workType "article" @default.