Derivation of Differential Geometry Theorems in High Dimensional Spaces
Journal: Region - Educational Research and Reviews DOI: 10.32629/rerr.v6i2.1731
Abstract
This research focuses on differential geometry in high-dimensional space, an area of great importance in revealing the structure of the universe and the properties of microscopic particles. Through precise mathematical modeling and in-depth theoretical analysis, this paper successfully deduces and validates a series of key high-dimensional differential geometry theorems, and discusses their application in specific high-dimensional Spaces. The results not only deepen our understanding of the interaction between curvature and topology in high-dimensional Spaces, but also demonstrate the potential applications of these theorems in mathematical physics, especially in general relativity and quantum gravity. These findings provide a new perspective for the theoretical development of high-dimensional differential geometry, and promote the depth of scientific exploration and interdisciplinary cooperation.
Keywords
high dimensional space, differential geometry, geometric theorem
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[2] Frittelli, S., Kozameh, C., Newman, E. T. Differential geometry from differential equations. Communications in Mathematical Physics. 2001; 223(2): 383-408.
[3] Rosensteel, George. Differential geometry of collective models. AIMS Mathematics. 2019; 4(2): 215-230.
[4] Deolindo Silva, Jorge Luiz, Tari Farid. On the Differential Geometry of Holomorphic Plane Curves. Transactions of the American Mathematical Society. 2020; 373(10): 6817-6833.
[5] Falkensteiner Sebastian, Garay Lopez, Cristhian Haiech, Mercedes Noordman, Marc Paul, Boulier Francois, Toghani Zeinab. On initials and the fundamental theorem of tropical partial differential algebraic geometry. Journal of Symbolic Computation. 2023; 115: 53-73.
[6] Brustad, Karl K. Segre’s Theorem. An Analytic Proof of a Result in Differential Geometry. Asian Journal of Mathematics. 2021; 25(3): 321-340.
[7] Zhou Chen. A new proof of Huber’s theorem on differential geometry in the large. Geometriae Dedicata. 2023; 217(3): 48.
[8] Magnot, Jean-Pierre. On the differential geometry of numerical schemes and weak solutions of functional equations. Nonlinearity. 2020; 33(12): 6835-6867.
[9] Khadjiev Djavvat, Ören Idris, Peksen Omer. Generating systems of differential invariants and the theorem on existence for curves in the pseudo-Euclidean geometry. Turkish Journal of Mathematics. 2013; 37(1): 80-94.
[10] Klein Sebastian. Differential Geometry and its Applications. Differential Geometry and its Applications. 2017; 54: 129-149.
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