Geometric Realizations of Curvature is popular PDF and ePub book, written by Miguel Brozos-Vázquez in 2012, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Geometric Realizations of Curvature can be Read Online from any device for your convenience.
Geometric Realizations of Curvature Book PDF Summary
A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are reviewed and presented in a clear, coherent form, including the latest developments and proofs. Even though many authors have worked in this area in recent years, many fundamental questions still remain unanswered. Many studies begin by first working purely algebraically and then later progressing onto the geometric setting and it has been found that many questions in differential geometry can be phrased as problems involving the geometric realization of curvature. Curvature decompositions are central to all investigations in this area. The authors present numerous results including the Singer Thorpe decomposition, the Bokan decomposition, the Nikcevic decomposition, the Tricerri Vanhecke decomposition, the Gray Hervella decomposition and the De Smedt decomposition. They then proceed to draw appropriate geometric conclusions from these decompositions. The book organizes, in one coherent volume, the results of research completed by many different investigators over the past 30 years. Complete proofs are given of results that are often only outlined in the original publications. Whereas the original results are usually in the positive definite (Riemannian setting), here the authors extend the results to the pseudo-Riemannian setting and then further, in a complex framework, to para-Hermitian geometry as well. In addition to that, new results are obtained as well, making this an ideal text for anyone wishing to further their knowledge of the science of curvature.
Detail Book of Geometric Realizations of Curvature PDF
- Author : Miguel Brozos-Vázquez
- Release : 21 September 2024
- Publisher : World Scientific
- ISBN : 9781848167414
- Genre : Mathematics
- Total Page : 263 pages
- Language : English
- PDF File Size : 8,6 Mb
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