WebChern and Lashof ([1], [2]) conjectured that if a smooth manifoldM m has an immersion intoR w, then the best possible lower bound for its total absolute cu A proof of the Chern … We would like to show you a description here but the site won’t allow us. WebMar 1, 2013 · As a special case, we have the horo-spherical Chern-Lashof type inequality and horo-tight immersions in the hyperbolic space [1,2, 15]. Motivated by those arguments, we can introduce the notion of ...
The Lipschitz-Killing curvature for an equiaffine immersion …
WebChern and Lashof [1] proved several inequalities concerning the total cur vature of an immersed manifold. Their second result is a weak generalization of the Fary-Milnor theorem [2], [5] for closed space curves. In this paper, a stronger result (Corollary 1), the complete homotopy extension, is stated and proved. WebShiing-Shen Chern ( / tʃɜːrn /; Chinese: 陳省身; pinyin: Chén Xǐngshēn, Mandarin: [tʂʰən.ɕiŋ.ʂən]; October 28, 1911 – December 3, 2004) was a Chinese-American mathematician and poet. He made fundamental … men\u0027s long polo shirts
Geometry of immersed manifolds - Encyclopedia of Mathematics
WebAbstract In this paper, we prove the theorems of the Gauss-Bonnet and Chern-Lashof types for low dimensional compact submanifolds in a simply connected symmetric space of compact type. In particular, in the case where the ambient space is a sphere, we need not to give the restriction for the dimension of the submanifold. WebTOTAL ABSOLUTE HOROSPHERICAL CURVATURE OF SUBMANIFOLDS IN HYPERBOLIC SPACE MARCELO BUOSI, SHYUICHI IZUMIYA, AND MARIA APARECIDA SOARES RUAS Abstract. We study the horospherical ge WebChern{Lashof [6] proved that a closed surface in R3 of non-negative Gauss curvature is the boundary of a weakly convex body. For n 2, Sacksteder [20] proved that a hypersurface with non-negative sectional curvature has semi-positive de nite second funda-mental form. His proof used the earlier results of van Heijenoort [10] and Hartman{Nirenberg ... men\\u0027s long raincoat with removable liner