منابع مشابه
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Warped products provide perhaps the major source of examples and counterexamples in metric and Riemannian geometry. Sufficient conditions for a warped product B×f F to have a curvature bound in the sense of Alexandrov, either above or below, are found in [AB 04]. Given the importance of warped products, we want to know if all the known sufficient conditions are needed. Here we prove their neces...
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We discuss the conformal boundary of a warped product of two length spaces and provide a method to calculate this in terms of the individual conformal boundaries. This technique is then applied to produce CAT(0)-spaces with complicated conformal boundaries. Finally we prove that the conformal boundary of an Hadamard n-manifold is always simply connected for n ≥ 3, thus providing a bound for the...
متن کاملA Ddvv Inequality for Submanifolds of Warped Products
We prove a DDVV inequality for submanifolds of warped products of the form I ×a Mn(c) where I is an interval and Mn(c) a real space form of curvature c . As an application, we give a rigidity result for submanifolds of R×eλt Hn(c). RÉSUMÉ. Une inégalité de type DDVV pour les sous-variétés des produits tordus. Nous donnons une inégalité de type DDVV pour les sous-variétés des produits tordus de ...
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2007
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2006.09.002