Elementary Differential Geometry

By Christian Bär. 2010

903 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Geometry and Topology, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/6816db947aba0d7639950e6146c49a6e02892f91

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In Biomedical Engineering

In Geometry and Topology

In Theoretical Computer Science

Citations in the corpus

A Quadrature Formula for Diffusion Polynomials Corresponding to a Generalized Heat Kernel (2010, background): “We will avoid very technical details, which can be found in such standard texts as [3, 4, 5, 31].”
Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium (2016, background): “Besides, the squared Frenet curvature, k2, of the beam axis in the present configuration, with some algebra from the definition [76], is related to the beam curvature κ2 = c⊥ · c⊥ by the expression: [k(S)](2) = c⊥ · c⊥ ‖χ′ (S)‖(2) .”
Interpolation among reduced‐order matrices to obtain parameterized models for design, optimization and probabilistic analysis (2009, methodology): “[35] for interpolation of the POD basis vectors, we choose here to use the concept of a Riemannian manifold, originating from differential geometry [39, 40, 41].”
From flat sheets to curved geometries: Origami and kirigami approaches (2017, background): “This simple interpretation of the metric as a grid on the surface, though not mathematically rigorous, does provide the important insight that we are aiming for: changing the Gaussian curvature requires a change in the surface metric (this leads to the inherent challenge that map-makers face: any ma”
A Stochastic Optimal Power Flow Problem With Stability Constraints—Part I: Approximating the Stability Boundary (2013, background): “(12) The map is the Weingarten map [21] which is the differential of the Gauss map where is the unit sphere in , i.”