Results 1 to 10 of about 66,484 (87)

Generalized Sums over Histories for Quantum Gravity I. Smooth Conifolds [PDF]

, 1993
This paper proposes to generalize the histories included in Euclidean functional integrals from manifolds to a more general set of compact topological spaces.
Amsterdamski, Anderson, Besse, Coleman, DeWitt, Donald M. Witt, Freedman, Gao, Gell-Mann, Geroch, Gibbons, Giddings, Glimm, Halliwell, Halliwell, Halliwell, Hartle, Hartle, Hartle, Hawking, Hawking, Hawking, Hirsch, Kirby, Kobayashi, Kristin Schleich, Nash, Page, Polchinski, Reed, Rourke, Schleich, Schleich, Spanier, Thurston, Uhlenbeck, Witt, Wright   +37 more
core   +3 more sources

Exotic Spaces in Quantum Gravity I: Euclidean Quantum Gravity in Seven Dimensions [PDF]

, 1999
It is well known that in four or more dimensions, there exist exotic manifolds; manifolds that are homeomorphic but not diffeomorphic to each other. More precisely, exotic manifolds are the same topological manifold but have inequivalent differentiable ...
Aloff S, Carlip S, Donald Witt, Freedman M, Freund P, Gibbons G, Gibbons G W, Gromoll D, Hawking S W, Hawking S W, Hirsch M W, Kirby R, Kreck M, Kreck M, Kristin Schleich, Milnor J, Moise E, Press W, Wallach N, Wang M   +19 more
core   +4 more sources

A distance on curves modulo rigid transformations [PDF]

, 2014
We propose a geometric method for quantifying the difference between parametrized curves in Euclidean space by introducing a distance function on the space of parametrized curves up to rigid transformations (rotations and translations). Given two curves,
Eldering, Jaap, Vankerschaver, Joris
core   +1 more source

Marriages of Mathematics and Physics: A Challenge for Biology [PDF]

, 2017
The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century.
Islami, Arezoo, Longo, Giuseppe
core   +1 more source

Exploring quaternionic Bertrand curves: involutes and evolutes in $ \mathbb{E}^{4} $

AIMS Mathematics
This study investigated the concepts of (0, 2)-involute and (1, 3)-evolute curves associated with quaternionic Bertrand curves within the context of four-dimensional Euclidean space.
Ayman Elsharkawy, Ahmer Ali, Muhammad Hanif, Fatimah Alghamdi   +3 more
doaj   +1 more source

Intertwined Hamiltonians in Two Dimensional Curved Spaces

, 2004
The problem of intertwined Hamiltonians in two dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane,Minkowski plane, Poincar{\' e} half plane ($AdS_2$), de Sitter Plane ($dS_2$), sphere, and torus. It is shown that
Aghababaei Samani, Aghababaei Samani, Bakalov, Balazs, Cariñena, Cooper, Demircioğlu, Dobrev, Gutzwillwer, Kalnins, Keivan Aghababaei Samani, Kuru, Mateev, Milanoviv, Mina Zarei, Mostafazadeh   +15 more
core   +2 more sources

AI-Powered Approaches for Hypersurface Reconstruction in Multidimensional Spaces

Mathematics
The present article explores the possibilities of using artificial neural networks to solve problems related to reconstructing complex geometric surfaces in Euclidean and pseudo-Euclidean spaces, examining various approaches and techniques for training ...
Kostadin Yotov, Emil Hadzhikolev, Stanka Hadzhikoleva, Mariyan Milev   +3 more
doaj   +1 more source

On post-Lie algebras, Lie--Butcher series and moving frames

, 2013
Pre-Lie (or Vinberg) algebras arise from flat and torsion-free connections on differential manifolds. They have been studied extensively in recent years, both from algebraic operadic points of view and through numerous applications in numerical analysis,
A. Connes, A. Iserles, A. Lundervold, A. Lundervold, A. Zanna, A.A. Agrachev, Alexander Lundervold, B. Owren, B. Vallette, C. Brouder, C. Reutenauer, D. Lewis, D. Lewis, E. Celledoni, E. Hairer, E.B. Vinberg, E.L. Mansfield, F. Chapoton, H. Berland, H. Munthe-Kaas, H. Munthe-Kaas, H. Munthe-Kaas, H. Munthe-Kaas, H. Munthe-Kaas, H. Munthe-Kaas, H. Munthe-Kaas, Hans Z. Munthe-Kaas, J.C. Butcher, J.C. Butcher, J.C. Novelli, J.L. Loday, K.C.H. Mackenzie, M. Degeratu, M. Fels, M. Fels, M. Gerstenhaber, M. Goze, N. Jacobson, P.E. Crouch, P.J. Olver, R. Grossman, R.B. Gardner, R.W. Sharpe, S. Kobayashi   +43 more
core   +2 more sources

Quasiconformal mappings on the Grushin plane

, 2017
We prove that a self-homeomorphism of the Grushin plane is quasisymmetric if and only if it is metrically quasiconformal and if and only if it is geometrically quasiconformal.
Gartland, Chris, Jung, Derek, Romney, Matthew   +2 more
core   +1 more source

Convergence of vector bundles with metrics of Sasaki-type

, 2011
If a sequence of Riemannian manifolds, $X_i$, converges in the pointed Gromov-Hausdorff sense to a limit space, $X_\infty$, and if $E_i$ are vector bundles over $X_i$ endowed with metrics of Sasaki-type with a uniform upper bound on rank, then a ...
B. Wilking, C.L. Terng, D. Burago, D. Gromoll, E. Boeckx, E. Musso, J. Cheeger, J. Cheeger, J. Cheeger, J. Cheeger, J. Cheeger, J. Cheeger, K. Grove, M. Benyounes, M. Gromov, M. Gromov, M.A. Rieffel, M.T. Anderson, M.T. Anderson, M.T. Kadaoui Abbassi, O. Kowalski, O. Kowalski, P. Petersen, P. Solórzano, P.J. Freyd, Pedro Solórzano, S. Kobayashi, S. Sasaki, T. Shioya, T. Yamaguchi, X. Rong   +30 more
core   +1 more source