Bochner's Formula
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U R (where U is an open subset of Rn) which satisfies Laplace''s equation, i.e. In Riemannian geometry, a Riemannian manifold or Riemannian space (M,g) is a real differentiable manifold M in which each tangent space is equipped with an inner product g, a Riemannian metric, in a manner which varies smoothly from point to…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U R (where U is an open subset of Rn) which satisfies Laplace''s equation, i.e. In Riemannian geometry, a Riemannian manifold or Riemannian space (M,g) is a real differentiable manifold M in which each tangent space is equipped with an inner product g, a Riemannian metric, in a manner which varies smoothly from point to point. The metric g is a positive definite symmetric tensor: a metric tensor. This allows one to define various notions such as angles, lengths of curves, areas (or volumes), curvature, gradients of functions and divergence of vector fields. In other words, a Riemannian manifold is a differentiable manifold in which the tangent space at each point is a finite-dimensional Euclidean space. The terms are named after German mathematician Bernhard Riemann.