Aspects of Differential Geometry III

Aspects of Differential Geometry III

Esteban Calvino-Louzao, Eduardo Garcia-Rio, Peter Gilkey, JeongHyeong Park, Ramon Vazquez-Lorenzo
ISBN: 9781627056861 | PDF ISBN: 9781627058827
Copyright © 2017 | 160 Pages | Publication Date: May, 2017

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Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book III is aimed at the first-year graduate level but is certainly accessible to advanced undergraduates. It deals with invariance theory and discusses invariants both of Weyl and not of Weyl type; the Chern-Gauss-Bonnet formula is treated from this point of view. Homothety homogeneity, local homogeneity, stability theorems, and Walker geometry are discussed. Ricci solitons are presented in the contexts of Riemannian, Lorentzian, and affine geometry.

Table of Contents

Preface
Acknowledgments
Invariance Theory
Homothety Homogeneity and Local Homogeneity
Ricci Solitons
Bibliography
Authors' Biographies
Index

About the Author(s)

Esteban Calvino-Louzao, University of Santiago de Compostela, Spain
Esteban is a member of the research group in Riemannian Geometry at the Department of Geometry and Topology of the University of Santiago de Compostela (Spain). He received his Ph.D. in 2011 under the direction of E. Garcia-Rio and R. Vazquez-Lorenzo. His research specialty is Riemannian and pseudo-Riemannian geometry. He has published more than 20 research articles and books.

Eduardo Garcia-Rio, University of Santiago de Compostela, Spain
Eduardo is a Professor of Mathematics at the University of Santiago (Spain). He is a member of the editorial board of Differential Geometry and its Applications and The Journal of Geometric Analysis and leads the research group in Riemannian Geometry at the Department of Geometry and Topology of the University of Santiago de Compostela (Spain). He received his Ph.D. in 1992 from the University of Santiago under the direction of A. Bonome and L. Torron. His research specialty is Differential Geometry. He has published more than 120 research articles and books.

Peter Gilkey, University of Oregon
Peter is a Professor of Mathematics and a member of the Institute of Theoretical Science at the University of Oregon. He is a fellow of the American Mathematical Society and is a member of the editorial board of Results in Mathematics, Differential Geometry and its Applications, and The Journal of Geometric Analysis. He received his Ph.D. in 1972 from Harvard University under the direction of L. Nirenberg. His research specialties are Differential Geometry, Elliptic Partial Differential Equations, and Algebraic topology. He has published more than 260 research articles and books.

JeongHyeong Park, SungKyunkan University, Korea
JeongHyeong is a Professor of Mathematics at Sungkyunkan University and is an associate member of he KIAS Korea).She received her Ph.D. in 1990 from Kanazawa University in Japan under the direction of H. Kitahara. Her research specialties are spectral geometry of Riemannian submersion and geometric structures on manifolds like eta-Einstein manifolds and H-contact manifolds. She organized the geometry section of AMC 2013 (The Asian Mathematical Conference 2013), the ICM 2014 satellite conference on Geometric analysis, and geometric structures on manifolds (2016). She has published more than 81 research articles and books.

Ramon Vazquez-Lorenzo, University of Santiago de Compostela, Spain
Ramon is a member of the research group in Riemannian Geometry at the Department of Geometry and Topology of the University of Santiago de Compostela (Spain). He is a member of the Spanish Research Network on Relativity and Gravitation. He received his Ph.D. in 1997 from the University of Santiago de Compostela under the direction of E. Garcia-Rio. His research focuses mainly on Differential Geometry with special emphasis on the study of the curvature and the algebraic properties of curvature operators in the Lorentzian and in the higher signature settings. He has published more than 50 research articles and books.

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