Jurgen Berndt, Sergio Console, Carlos Enrique Olmos

Submanifolds and Holonomy

• Gebundenes Buch

Produktbeschreibung

This second edition explores recent progress in the submanifold geometry of space forms, including new methods based on the holonomy of the normal connection. It contains five new chapters on the normal holonomy of complex submanifolds, the Berger-Simons holonomy theorem, the skew-torsion holonomy theorem, and polar actions on symmetric spaces of compact type and noncompact type. It also includes several new sections on orbits for isometric actions, geodesic submanifolds, and symmetric spaces.

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Produktdetails

• Chapman & Hall/CRC Monographs and Research Notes in Mathematics
• Verlag: Taylor & Francis Inc
• 2 ed
• Seitenzahl: 496
• Erscheinungstermin: 8. Februar 2016
• Englisch
• Abmessung: 240mm x 161mm x 31mm
• Gewicht: 838g
• ISBN-13: 9781482245158
• ISBN-10: 1482245159
• Artikelnr.: 43922801

Autorenporträt

Jürgen Berndt is a professor of mathematics at King's College London. He is the author of two research monographs and more than 50 research articles. His research interests encompass geometrical problems with algebraic, analytic, or topological aspects, particularly the geometry of submanifolds, curvature of Riemannian manifolds, geometry of homogeneous manifolds, and Lie group actions on manifolds. He earned a PhD from the University of Cologne. Sergio Console (1965-2013) was a researcher in the Department of Mathematics at the University of Turin. He was the author or coauthor of more than 30 publications. His research focused on differential geometry and algebraic topology. Carlos Enrique Olmos is a professor of mathematics at the National University of Cordoba and principal researcher at the Argentine Research Council (CONICET). He is the author of more than 35 research articles. His research interests include Riemannian geometry, geometry of submanifolds, submanifolds, and holonomy. He earned a PhD from the National University of Cordoba.

Inhaltsangabe

Basics of Submanifold Theory in Space Forms. Submanifold Geometry of
Orbits. The Normal Holonomy Theorem. Isoparametric Submanifolds and Their
Focal Manifolds. Rank Rigidity of Submanifolds and Normal Holonomy of
Orbits. Homogeneous Structures on Submanifolds. Normal Holonomy of Complex
Submanifolds. The Berger-Simons Holonomy Theorem. The Skew-Torsion Holonomy
Theorem. Submanifolds of Riemannian Manifolds. Submanifolds of Symmetric
Spaces. Polar Actions on Symmetric Spaces of Compact Type. Polar Actions on
Symmetric Spaces of Noncompact Type. Appendix.