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Frame bundle
About: Frame bundle is a research topic. Over the lifetime, 1600 publications have been published within this topic receiving 23049 citations.
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TL;DR: In this paper, the authors constructed rotationally symmetric Kahler-Ricci solitons on the total space of direct sum of fixed hermitian line bundle and its projective compactification.
Abstract: In this note, using Calabi's method, we construct rotationally symmetric Kahler-Ricci solitons on the total space of direct sum of fixed hermitian line bundle and its projective compactification, where the curvature of hermitian line bundle is Kahler-Einstein. These examples generalize the construction of Koiso, Cao and Feldman-Ilmanen-Knopf.
18 citations
18 citations
TL;DR: In this paper, a general notion of connections over a vector bundle map is considered, and applied to the study of mechanical systems with linear nonholonomic constraints and a Lagrangian of kinetic energy type.
Abstract: A general notion of connections over a vector bundle map is considered, and applied to the study of mechanical systems with linear nonholonomic constraints and a Lagrangian of kinetic energy type. In particular, it is shown that the description of the dynamics of such a system in terms of the geodesics of an appropriate connection can be easily recovered within the framework of connections over a vector bundle map. Also the reduction theory of these systems in the presence of symmetry is discussed from this perspective.
18 citations
TL;DR: In this paper, the spectral geometry of the twisted Dirac operator was analyzed in terms of the natural holomorphic structures of the spinor bundles E ± defined by the Cauchy-Riemann operators associated with the spinorial connection.
18 citations
Posted Content•
TL;DR: In this article, the authors extend the notion of a Parseval frame for a fixed Hilbert space to that of a movingParseval Frame for a vector bundle over a manifold, and prove that a sequence of vector fields is a moving Parsevel Frame for the tangent bundle of a Riemannian manifold if and only if the vector fields are the orthogonal projection of the moving orthonormal basis for a larger vector bundle.
Abstract: Parseval frames can be thought of as redundant or linearly dependent coordinate systems for Hilbert spaces, and have important applications in such areas as signal processing, data compression, and sampling theory. We extend the notion of a Parseval frame for a fixed Hilbert space to that of a moving Parseval frame for a vector bundle over a manifold. Many vector bundles do not have a moving basis, but in contrast to this every vector bundle over a paracompact manifold has a moving Parseval frame. We prove that a sequence of sections of a vector bundle is a moving Parseval frame if and only if the sections are the orthogonal projection of a moving orthonormal basis for a larger vector bundle. In the case that our vector bundle is the tangent bundle of a Riemannian manifold, we prove that a sequence of vector fields is a Parseval frame for the tangent bundle of a Riemannian manifold if and only if the vector fields are the orthogonal projection of a moving orthonormal basis for the tangent bundle of a larger Riemannian manifold.
18 citations