Immersions in Warped Product Spaces
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Beschreibung
This book offers a detailed exploration of the intrinsic geometrical properties of warped product spaces through the lens of mathematical analysis and global differential geometry. It touches upon key topics such as uniqueness results, height estimates, Riemannian immersions, and the geometrical behavior of submanifolds, while addressing complex phenomena that challenge traditional Euclidean assumptions. Divided into five comprehensive parts, the text provides clear refinements of recent findings, with connections to General Relativity and semi-Riemannian geometry.
Accessible yet thorough, this monograph is ideal for post-graduate students, researchers, and specialists across mathematics, geometry, and theoretical physics.
This book offers a detailed exploration of the intrinsic geometrical properties of warped product spaces through the lens of mathematical analysis and global differential geometry. It touches upon key topics such as uniqueness results, height estimates, Riemannian immersions, and the geometrical behavior of submanifolds, while addressing complex phenomena that challenge traditional Euclidean assumptions. Divided into five comprehensive parts, the text provides clear refinements of recent findings, with connections to General Relativity and semi-Riemannian geometry.
Accessible yet thorough, this monograph is ideal for post-graduate students, researchers, and specialists across mathematics, geometry, and theoretical physics.
Focuses on Warped Product Spaces and their applications in Semi-Riemannian Geometry Explores connections to General Relativity, making the book relevant for in recent advances in physics and geometry Adopts a pedagogical approach by including background information and prioritizing clarity
Autor*in
Henrique Fernandes de Lima
Themen in »Immersions in Warped Product Spaces«
Generalized Robertson-Walker spacetime complete spacelike mean curvature flow solitons Einstein-de Sitter spacetime steady state type spacetimes de Sitter and anti-de Sitter spaces Calabi-Bernstein type results drift Laplacian Bakry-Émery Ricci tensor weighted semi-Riemmanian warped products codimension reduction of submanifolds bifurcation and local rigidity of hypersurfaces stability of compact hypersurfaces height estimates and half-space type results
Stimmen zu »Immersions in Warped Product Spaces«
“This monograph is a substantial and carefully crafted contribution to the theory of submanifolds and hypersurfaces in warped products. It successfully integrates classical submanifold geometry, Lorentzian geometry, weighted manifolds, stability theory, and bifurcation analysis into a single coherent framework. ... Researchers working in Riemannian or Lorentzian geometry, geometric analysis, and mathematical physics will find this monograph to be a valuable reference. It also offers a rich source of ideas and techniques for advanced graduate students entering the field.” (Gabriel Eduard Vilcu, zbMATH 1577.53004, 2026)
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