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- W1584331691 abstract "Let Mn be an n-dimensional Riemannian manifold which is minimally immersed in a unit sphere Sn+P(l) of dimension n+p. Then the second fundamental form h of the immersion is given by h{X, Y)=1XY―1 xY and it satisfies h{X, Y)―h(Y, X), where 7 and 7 denote the covariant differentiationon Sn+P(l) and Mn respectively, X and Y are vector fields on Mn. We choose a local field of orthonormal frames eu ・・・,en, ■■■, en+p in Sn+P(l) such that, restricted to Mn, the vector eu ・■・,en are tangent to Mn. We use the following convention on the range of indices unless otherwise stated: A, B, C, ・・・=!, 2, ・・・, n+p; i, j, k, ■・・=!,2, ・・・, n; a, j8,■■・ = n+l, ・■・,n+p. And we agree that repeated indices under a summation sign without indication are summed over the respective range. With respect to the frame fieldof Sn+P(l) chosen above, let <5i,・■・,aJn+p be the dual frames. Then structure equations of Sn+P(l) are given by" @default.
- W1584331691 created "2016-06-24" @default.
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- W1584331691 date "1989-06-01" @default.
- W1584331691 modified "2023-10-18" @default.
- W1584331691 title "Complete Riemannian manifold minimally immersed in a unit sphere $S^{n+p} (1)$" @default.
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- W1584331691 doi "https://doi.org/10.21099/tkbjm/1496161010" @default.
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