This book deals with Riemannian manifolds for which the nullity space of the curvature tensor has codimension two. These manifolds are "semi-symmetric spaces foliated by Euclidean leaves of codimension two" in the sense of Z.I. Szabo. The authors concentrate on the rich geometrical structure and explicit descriptions of these remarkable spaces. Also parallel theories are developed for manifolds of "relative conullity two". This makes a bridge to a survey on curvature homogeneous spaces introduced by I.M. Singer. As an application of the main topic, interesting hypersurfaces with type number two in Euclidean space are discovered, namely those which are locally rigid or "almost rigid". The unifying method is solving explicitly particular systems of nonlinear PDE.
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Inside This Book
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First Sentence:
Let (M, g) be an n-dimensional Riemannian manifold and OM its principal bundle of orthonormal frames. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Levi Civita, Proof According, Proof Let, Euclidean Jordan, Proof First, Proof Substituting, Proof Suppose New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Let (M, g) be an n-dimensional Riemannian manifold and OM its principal bundle of orthonormal frames. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Levi Civita, Proof According, Proof Let, Euclidean Jordan, Proof First, Proof Substituting, Proof Suppose New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
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cites this book:
- Exterior Differential Systems (Mathematical Sciences Research Institute Publications) by Robert L. Bryant in Back Matter
- Non-Euclidean Geometries: János Bolyai Memorial Volume (Mathematics and Its Applications) by András Prékopa on page 425, and page 426
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