Volumes of Tubes About Complex Submanifolds of Complex Projective Space

DOI10.2307/2000094zbMath0575.53043OpenAlexW4256490849MaRDI QIDQ3695966

Alfred Gray

Publication date: 1985

Full work available at URL: https://doi.org/10.2307/2000094

zbMATH Keywords

Chern classesKähler submanifoldcomplex submanifoldsvolume of a tubeBishop-Gunther comparison theorem

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55)

Related Items (10)

On the total curvature and Betti numbers of complex projective manifolds ⋮ Unnamed Item ⋮ Hausdorff approximations and volume of tubes of singular algebraic sets ⋮ Upper bounds for the first Dirichlet eigenvalue of a tube around an algebraic complex curve of \(\mathbb C\mathbb{P}^{n}(\lambda)\) ⋮ Integral geometry of complex space forms ⋮ Bounding the first Dirichlet eigenvalue of a tube around a complex submanifold of \(\mathbb CP^n(\lambda)\) in terms of the degrees of the polynomials defining it ⋮ Volume estimate for a cone with a submanifold as vertex ⋮ Brownian motion and Riemannian geometry in the neighbourhood of a submanifold ⋮ Upper bounds on the distribution of the condition number of singular matrices ⋮ Comparison theorems for the volume of a complex submanifold of a Kaehler manifold

Cites Work

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• Comparison theorems for the volumes of tubes as generalizations of the Weyl tube formula
• Complex differential and integral geometry and curvature integrals associated to singularities of complex analytic varieties
• A generalization of F. Schur's theorem
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• The volume of a tube in complex projective space
• Characteristic Classes. (AM-76)
• Chern Numbers and Curvature
• The Volume of Tubes in Complex Projective Space
• On the Volume of Tubes

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