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Notes on infinitesimal variations of submanifolds

DOI: 10.1016/s0304-0208(08)72258-8


Publisher Summary Submanifolds under consideration are compact and orientable and using integral formulas, some global results on infinitesimal isometric, affine and conformal variations of the submanifolds, are obtained. Infinitesimal variations, infinitesimal affine variations and infinitesimal conformal variations are discussed. If the variation is conformal and R is a constant, the infinitesimal variation is homothetic. If an infinitesimal affine variation of a compact orientable submanifold of a Rieiizannian manifold satisfies then the variation is an isometry.

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