On Chern's kinematic formula in integral geometry
نویسندگان
چکیده
منابع مشابه
A uniform reconstruction formula in integral geometry
A new method for analytic inversion of Radon type integral transforms is proposed. Key words: Regular hypersurface family, Funk-Radon transform, Principal value integral, Reconstruction, Hyperbolic algebraic curve MSC 53C65 44A12 65R10 1 Introduction We present a uniform reconstruction method for a class of geometric integral transforms for submanifolds of codimension 1. The reconstruction does...
متن کاملAn Integral Formula in Kahler Geometry with Applications
We establish an integral formula on a smooth, precompact domain in a Kahler manifold. We apply this formula to study holomorphic extension of CR functions. Using this formula we prove an isoperimetric inequality in terms of a positive lower bound for the Hermitian curvature of the boundary. Combining with a Minkowski type formula on the complex hyperbolic space we prove that any closed, embedde...
متن کاملA Gaussian Kinematic Formula
In this paper, we consider smooth, real-valued random fields built up from i.i.d. copies of centered, unit variance smooth Gaussian fields on a manifold M . Specifically, we consider random fields of the form fp = F (y1(p), . . . , yk(p)) for F ∈ C(R;R) and (y1, . . . , yk) a vector of C centered, unit-variance Gaussian fields. For fields of this type, we compute the expected Euler characterist...
متن کاملA lecture on integral geometry
Integral geometry originated from geometric probability. It studies random geometric objects in a probability space endowed with a measure that is invariant under a group of transformations. The geometric objects are points, lines, planes, solids, curves, surfaces, geodesics, etc. Works of Crofton, Poincaré, Sylvester, and others set up the early stage of integral geometry. Poincaré defined the...
متن کاملThe Kinematic Formula in Riemannian Homogeneous Spaces
Let G be a Lie group and K a compact subgroup of G. Then the homogeneous space G/K has an invariant Riemannian metric and an invariant volume form ΩG. Let M and N be compact submanifolds of G/K, and I(M ∩ gN) an “integral invariant” of the intersection M ∩ gN . Then the integral
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1974
ISSN: 0022-040X
DOI: 10.4310/jdg/1214432423