Osserman Manifolds in Semi-Riemannian Geometry

1. Front Matter

   Pages I-XII

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2. 1. The Osserman Conditions in Semi-Riemannian Geometry

   • Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo

   Pages 1-20

3. 2. The Osserman Conjecture in Riemannian Geometry

   • Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo

   Pages 21-37

4. 3. Lorentzian Osserman Manifolds

   • Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo

   Pages 39-61

5. 4. Four-Dimensional Semi-Riemannian Osserman Manifolds with Metric Tensors of Signature (2,2)

   • Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo

   Pages 63-94

6. 5. Semi-Riemannian Osserman Manifolds

   • Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo

   Pages 95-136

7. 6. Generalizations and Osserman-Related Conditions

   • Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo

   Pages 137-156

8. References

   • Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo

   Pages 157-163

9. Index

   • Eduardo García-Río, Demir N. Kupeli, Ramón Vázquez-Lorenzo

   Pages 165-166

10. Back Matter

    Pages 167-169

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The subject of this book is Osserman semi-Riemannian manifolds, and in particular, the Osserman conjecture in semi-Riemannian geometry. The treatment is pitched at the intermediate graduate level and requires some intermediate knowledge of differential geometry. The notation is mostly coordinate-free and the terminology is that of modern differential geometry. Known results toward the complete proof of Riemannian Osserman conjecture are given and the Osserman conjecture in Lorentzian geometry is proved completely. Counterexamples to the Osserman conjuncture in generic semi-Riemannian signature are provided and properties of semi-Riemannian Osserman manifolds are investigated.

• Osserman Conjecture
• Osserman Semi-Riemannian Manifold
• Riemannian geometry
• differential geometry
• manifold
• two-point homogeneous spaces

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