منابع مشابه
Minimal volume and simplicial norm of visibility n-manifolds and compact 3-manifolds
In this survey paper, we shall derive the following result. Theorem A. Let M denote a closed Riemannian manifold with nonpositive sectional curvature and let M̃ be the universal cover of M with the lifted metric. Suppose that the universal cover M̃ contains no totally geodesic embedded Euclidean plane R (i.e., M is a visibility manifold ). Then Gromov’s simplicial volume ‖M‖ is non-zero. Conseque...
متن کاملMinimal volume and simplicial norm of visibility n-manifolds and all 3-manifolds
In this paper, we present an elementary proof of the following result. Theorem A. Let Mn denote a closed Riemannian manifold with nonpositive sectional curvature and let M̃n be the universal cover of Mn with the lifted metric. Suppose that the universal cover M̃n contains no totally geodesic embedded Euclidean plane R2 (i.e., Mn is a visibility manifold ). Then Gromov’s simplicial volume ∥Mn∥ is ...
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(a) (b) Figure 8: The nal set of directions from that covers G S in thick gray lines. Two views are provided with (a) presents the regular view of Figures 5 to 7 and (b) shows the entire Gauss map. See also Figure 1. (a) (b) Figure 6: The boundary and central silhouettes of G S in thick dark gray lines is projected onto the plane z = 1 in thick light gray lines, in (a). In (b), The convex hull ...
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The object of the present paper is to introduce and study a type of non-flat semi-Riemannian manifolds, called, super generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [A.A. Shaikh and A. Patra, On a generalized class of recurrent manifolds, Arch. Math. (Brno) 46 (2010) 71--78.] and weakly generalized recurrent manifolds ...
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In this paper we try to extend geometric concepts in the context of operator valued tensors. To this end, we aim to replace the field of scalars $ mathbb{R} $ by self-adjoint elements of a commutative $ C^star $-algebra, and reach an appropriate generalization of geometrical concepts on manifolds. First, we put forward the concept of operator-valued tensors and extend semi-Riemannian...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1973
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1973.46.45