Prescribing mean curvature: existence and uniqueness problems.
Kamberov, G. (1998)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Kamberov, G. (1998)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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In this paper we study the pairs of orthogonal foliations on oriented surfaces immersed in R whose singularities and leaves are, respectively, the umbilic points and the lines of normal mean curvature of the immersion. Along these lines the immersions bend in R according to their normal mean curvature. By analogy with the closely related Principal Curvature Configurations studied in [S-G], [GS2], whose lines produce the extremal for the immersion, the pair of foliations by lines of...
Esmaeil Abedi, Reyhane Bahrami Ziabari, Mukut Mani Tripathi (2016)
Archivum Mathematicum
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We introduce a conformal Sasakian manifold and we find the inequality involving Ricci curvature and the squared mean curvature for semi-invariant, almost semi-invariant, -slant, invariant and anti-invariant submanifolds tangent to the Reeb vector field and the equality cases are also discussed. Also the inequality involving scalar curvature and the squared mean curvature of some submanifolds of a conformal Sasakian space form are obtained.