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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Similar results for Finsler spaces can be found in [1] and [3].
📌 3 Key Takeaways
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Objective & Hypothesis:A Cartan space is a pair (M, K), where M is a smooth manifold and K an Hamiltonean on the slit cotangent bundle $T_0^{star}$ M := TM{(x, 0), x$in$ M}, that is positively homogeneous of degree 1 in momenta.
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Key Findings & Data:We show that K induces an almost 2-paracontact Riemannian structure on $T_0^{star} M whose restriction to the figuratrix bundle $Bbb{K}$ = {(x,p) K(x,p) = 1} is an almost paracontact structure.
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Conclusion & Impact:Similar results for Finsler spaces can be found in [1] and [3].
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
A Cartan space is a pair (M, K), where M is a smooth manifold and K an Hamiltonean on the slit cotangent bundle $T_0^{star}$ M := TM{(x, 0), x$in$ M}, that is positively homogeneous of degree 1 in momenta. We show that K induces an almost 2-paracontact Riemannian structure on $T_0^{star} M whose restriction to the figuratrix bundle $Bbb{K}$ = {(x,p) K(x,p) = 1} is an almost paracontact structure. A condition for this almost para-contact structure to be normal is found, and its geometrical meaning is pointed out. Similar results for Finsler spaces can be found in [1] and [3].
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Cite This Article
GIRTU, M. (2022). An almost 2-paracontact structure on the cotangent bundle of a Cartan space. Hacettepe Journal of Mathematics and Statistics, Cilt: 33 - Sayı:, 15–22. https://ajindex.com/articles/530806