Results 91 to 100 of about 872 (123)

Differential Geometry and Matrix-Based Generalizations of the Pythagorean Theorem in Space Forms

Mathematics
In this work, we consider Pythagorean triples and quadruples using fundamental form matrices of hypersurfaces in three- and four-dimensional space forms and illustrate various figures. Moreover, we generalize that an immersed hypersphere Mn with radius r
Erhan Güler, Yusuf Yaylı, Magdalena Toda   +2 more
semanticscholar   +1 more source

Lecture Notes on Elementary Topology and Geometry.

, 1967
1 Some point set topology.- 1.1 Naive set theory.- 1.2 Topological spaces.- 1.3 Connected and compact spaces.- 1.4 Continuous functions.- 1.5 Product spaces.- 1.6 The Tychonoff theorem.- 2 More point set topology.- 2.1 Separation axioms.- 2.2 Separation ...
I. Singer, J. Thorpe
semanticscholar   +1 more source

Geometric Meta-Learning via Coupled Ricci Flow: Unifying Knowledge Representation and Quantum Entanglement

arXiv.org
This paper establishes a unified framework integrating geometric flows with deep learning through three fundamental innovations. First, we propose a thermodynamically coupled Ricci flow that dynamically adapts parameter space geometry to loss landscape ...
Ming Lei, C. Baehr
semanticscholar   +1 more source

Differential Geometry and Topology: With a View to Dynamical Systems

, 2005
MANIFOLDS Introduction Review of topological concepts Smooth manifolds Smooth maps Tangent vectors and the tangent bundle Tangent vectors as derivations The derivative of a smooth map Orientation Immersions, embeddings and submersions Regular and ...
K. Burns, M. Gidea
semanticscholar   +1 more source

An Introduction to Riemann-Finsler Geometry

, 2000
D. Bao, S. Chern, Z. Shen
semanticscholar   +1 more source

American Cancer Society's report on the status of cancer disparities in the United States, 2021

Ca-A Cancer Journal for Clinicians, 2022
Farhad Islami, Carmen E Guerra, K Robin Yabroff   +2 more
exaly  

Circles and spheres in pseudo-Riemannian geometry

, 1990
N. Abe, Y. Nakanishi, S. Yamaguchi
semanticscholar   +1 more source

On the problem whether the image of a given differentiable map into Riemannian manifold is contained in a submanifold with parallel second fundamental form.

, 1981
H. Reckziegel
semanticscholar   +1 more source

The Sub-Riemannian Curvature of Curves in the Borel Subgroup of the Group SL(2,ℝ)

Mathematical Notes, 2018
M. V. Tryamkin
semanticscholar   +1 more source

The Dirichlet problem and the inverse mean‐value theorem for a class of divergence form operators

Journal of the London Mathematical Society, 2013
Beatrice Abbondanza, A. Bonfiglioli
semanticscholar   +1 more source