This book, "Contact Manifolds in Riemannian Geometry," is a collection of lecture notes edited by A. Dold and B. Eckmann and authored by David E. Blair. It was published by Springer-Verlag in 1976 and is part of the Lecture Notes in Mathematics series (Vol. 509). The author, David E. Blair, is from the Department of Mathematics at Michigan State University. The book serves as an introduction to the subject of contact manifolds from a Riemannian geometry perspective, covering recent work and providing insights into the geometry of classical examples such as principal circle bundles and tangent sphere bundles. Key topics include: 1. **Contact Manifolds**: Definitions and basic properties. 2. **Almost Contact Manifolds**: Structural groups and the contact condition. 3. **Geometric Interpretation of the Contact Condition**: Integral submanifolds of the contact distribution. 4. **K-Contact and Sasakian Structures**: Normal almost contact structures, examples, and non-regular Sasakian structures. 5. **Sasakian Space Forms**: α-Sectional curvature, examples, and integral submanifolds. 6. **Non-Existence of Flat Contact Metric Structures**: Proof that no flat associated metric exists for contact manifolds of dimension ≥ 5. 7. **The Tangent Sphere Bundle**: Differential geometry and contact metric structure. The book includes references and an index, making it a comprehensive resource for researchers and students in Riemannian geometry and contact manifolds.This book, "Contact Manifolds in Riemannian Geometry," is a collection of lecture notes edited by A. Dold and B. Eckmann and authored by David E. Blair. It was published by Springer-Verlag in 1976 and is part of the Lecture Notes in Mathematics series (Vol. 509). The author, David E. Blair, is from the Department of Mathematics at Michigan State University. The book serves as an introduction to the subject of contact manifolds from a Riemannian geometry perspective, covering recent work and providing insights into the geometry of classical examples such as principal circle bundles and tangent sphere bundles. Key topics include: 1. **Contact Manifolds**: Definitions and basic properties. 2. **Almost Contact Manifolds**: Structural groups and the contact condition. 3. **Geometric Interpretation of the Contact Condition**: Integral submanifolds of the contact distribution. 4. **K-Contact and Sasakian Structures**: Normal almost contact structures, examples, and non-regular Sasakian structures. 5. **Sasakian Space Forms**: α-Sectional curvature, examples, and integral submanifolds. 6. **Non-Existence of Flat Contact Metric Structures**: Proof that no flat associated metric exists for contact manifolds of dimension ≥ 5. 7. **The Tangent Sphere Bundle**: Differential geometry and contact metric structure. The book includes references and an index, making it a comprehensive resource for researchers and students in Riemannian geometry and contact manifolds.