We introduce variational obstacle avoidance problems on Riemannian manifolds and derive necessary conditions for the existence of their normal extremals. The problem consists of minimizing an energy ...

Riemann Surface: A one-dimensional complex manifold that serves as the natural domain for studying holomorphic functions and forms the basis for many minimal surface constructions.

We propose a new knowledge graph completion model called MRME-KGC, based on multi-view Riemannian Manifolds fusion to achieve this. Specifically, MRME-KGC simultaneously considers the fusion of four ...

In 1926–27, Cartan gave a series of lectures in which he introduced exterior forms at the very beginning and used extensively orthogonal frames throughout to investigate the geometry of Riemannian ...

In this paper, we characterize three-dimensional Riemannian manifolds M 3 M 3 admitting Ricci–Yamabe solitons (RYSs). It is proved that if an M 3 M 3 endowed with a semi-symmetric metric ζ ζ ...

Published in Proceedings of the National Academy of Sciences Vol. 54 | No. 4October 15, 1965 PubMed: 16578615 ...

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The geometry of spacetime forms the very foundation of modern gravitational theory, where the elegant interplay between curvature and matter is described by Einstein’s field equations. In this ...

Researchers at Fraunhofer ILT, Aachen, Germany, have successfully additively manufactured a Ø720 x 100 mm³ Ni718 rocket engine manifold on its gantry-based Laser Beam Powder Bed Fusion (PBF-LB) AM ...

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Tensor analysis on manifolds by Richard L. Bishop Publication date 1980 Topics Calculus of tensors., Manifolds (Mathematics) Publisher Dover Publications Collection internetarchivebooks; inlibrary; ...