Curvature exponent and geodesic dimension on Sard-regular Carnot groups
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914890048864256 |
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| author | Golo, Sebastiano Nicolussi Zhang, Ye |
| author_facet | Golo, Sebastiano Nicolussi Zhang, Ye |
| contents | In this paper we characterize the geodesic dimension $N_{GEO}$ and give a new lower bound to the curvature exponent $N_{CE}$ on Sard-regular Carnot groups. As an application, we give an example of step-two Carnot group on which $N_{CE} > N_{GEO}$: this answers a question posed by Rizzi in arXiv:1510.05960v4 [math.MG]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_15811 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Curvature exponent and geodesic dimension on Sard-regular Carnot groups Golo, Sebastiano Nicolussi Zhang, Ye Metric Geometry Differential Geometry 53C17, 53C23 In this paper we characterize the geodesic dimension $N_{GEO}$ and give a new lower bound to the curvature exponent $N_{CE}$ on Sard-regular Carnot groups. As an application, we give an example of step-two Carnot group on which $N_{CE} > N_{GEO}$: this answers a question posed by Rizzi in arXiv:1510.05960v4 [math.MG]. |
| title | Curvature exponent and geodesic dimension on Sard-regular Carnot groups |
| topic | Metric Geometry Differential Geometry 53C17, 53C23 |
| url | https://arxiv.org/abs/2308.15811 |