PORTUGALIAEMATHEMATICA
Vol. 54, No. 2, pp. 139-145 (1997)
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PORTUGALIAE MATHEMATICA Vol. 54, No. 2, pp. 139-145 (1997) |
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Some Inequalities for Immersed SurfacesValery Marenich and Irwen Valle GuadalupeIMECC - UNICAMP, Universidade Estadual de Campinas,CP. 6065, 13081-970 Campinas, SP - BRASIL E-mail: marenich@ime.unicamp.br IMECC - UNICAMP, Universidade Estadual de Campinas, CP. 6065, 13081-970 Campinas, SP - BRASIL E-mail: irwen@ime.unicamp.br Abstract: For immersions of surfaces in Riemannian manifolds with pinched curvature we establish some generalizations of relations between the integral of the square of the norm of the mean curvature vector and the area of the surface with topological invariants, known for immersions into space forms. For immersions with codimension two into space forms of nonpositive curvature these leads to a nonexistence of minimal immersions with everywhere non-zero normal curvature tensor. Full text of the article:
Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.
© 1997 Sociedade Portuguesa de Matemática
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