Open AccessBook
Differential Geometry of Manifolds
Uday Chand De,Absos Ali Shaikh +1 more
TLDR
In this paper, differentiable manifolds are used to construct Fibre Bundles and Linear Connections, and Riemannian Manifolds and Submanifolds.Abstract:
Preface / Some Preliminaries / Differentiable Manifolds / Exterior Algebra and Exterior Derivative / Lie Group and Lie Algebras / Fibre Bundles / Linear Connections / Riemannian Manifolds / Submanifolds / Complex Manifolds / Bibliography / Index.read more
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A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
TL;DR: This paper introduces metric-based means for the space of positive-definite matrices and discusses some invariance properties of the Riemannian mean, and uses differential geometric tools to give a characterization of this mean.
Book
Geometric Mechanics and Symmetry: From Finite to Infinite Dimensions
TL;DR: Holm as mentioned in this paper provides a unified viewpoint of Lagrangian and Hamiltonian mechanics in the coordinate-free language of differential geometry in the spirit of the Marsden-Ratiu school.
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Minimal surfaces in porous media: Pore-scale imaging of multiphase flow in an altered-wettability Bentheimer sandstone.
TL;DR: High-resolution x-ray imaging was used in combination with differential pressure measurements to measure relative permeability and capillary pressure simultaneously during a steady-state waterflood experiment on a sample of Bentheimer sandstone, finding that the oil-brine interfaces were not flat, but had two approximately equal, but opposite, curvatures in orthogonal directions.
Book
Introduction to Tensor Analysis and the Calculus of Moving Surfaces
TL;DR: The Tensor Calculus of Moving Surfaces as discussed by the authors is a generalization of the tensor calculus of Euclidean spaces, and it has been used in many applications in differential geometry.
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Computation of the signed distance function to a discrete contour on adapted triangulation
TL;DR: A numerical method for computing the signed distance function to a discrete domain, on an arbitrary triangular background mesh mainly relies on the use of some theoretical properties of the unsteady Eikonal equation, and a way of adapting the mesh on which computations are held to enhance the accuracy.