This volume covers material presented by invited speakers at the AMS special session on Riemannian and Lorentzian geometries held at the annual Joint Mathematics Meetings in Baltimore. Topics covered include classification of curvature-related operators, curvature-homogeneous Einstein 4-manifolds, linear stability/instability singularity and hyperbolic operators of spacetimes, spectral geometry of holomorphic manifolds, cut loci of nilpotent Lie groups, conformal geometry of almost Hermitian manifolds, and also submanifolds of complex and contact spaces.

This volume can serve as a good reference source and provide indications for further research. It is suitable for graduate students and research mathematicians interested in differential geometry.

Readership

Graduate students and research mathematicians interested in differential geometry.

Table of Contents

• K. Abe, D. Grantcharov, and G. Grantcharov -- On some complex manifolds with torus symmetry
• M. J. S. L. Ashley and S. M. Scott -- Curvature singularities and abstract boundary singularity theorems for space-time
• A. Derdzinski -- Curvature-homogeneous indefinite Einstein metrics in dimension four: The diagonalizable case
• P. E. Ehrlich, Y.-T. Jung, J.-S. Kim, and S.-B. Kim -- Jacobians and volume comparison for Lorentzian warped products
• B. Fiedler and P. Gilkey -- Nilpotent Szabó, Osserman and Ivanov-Petrova pseudo-Riemannian manifolds
• P. B. Gilkey, R. Ivanova, and I. Stavrov -- Jordan Szabó algebraic covariant derivative curvature tensors
• A. D. Helfer -- Differential topology, differential geometry, and hyperbolic operators
• C. Jang and P. E. Parker -- Examples of conjugate loci of pseudoriemannian 2-step nilpotent Lie groups with nondegenerate center
• R. G. McLenaghan, R. G. Smirnov, and D. The -- Group invariant classification of orthogonal coordinate webs
• J. H. Park -- Spectral geometry and the Kaehler condition for Hermitian manifolds with boundary
• P. Rukimbira -- Energy, volume and deformation of contact metrics
• R. Sharma -- Holomorphically planar conformal vector fields on almost Hermitian manifolds
• B. D. Suceavă -- Fundamental inequalities and strongly minimal submanifolds
• M. Tanimoto -- Linear perturbations of spatially locally homogeneous spacetimes
• M. M. Tripathi -- Certain basic inequalities for submanifolds in \((\kappa,\mu)\)-spaces