Harmonic-hyperbolic geometric flow
In this article we study a coupled system for hyperbolic geometric flow on a closed manifold M, with a harmonic flow map from M to some closed target manifold N. Then we show that this flow has a unique solution for a short-time. After that, we find evolution equations for Riemannian curvature...
| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2017-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2017/165/abstr.html |
| _version_ | 1819267602145345536 |
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| author | Shahroud Azami |
| author_facet | Shahroud Azami |
| author_sort | Shahroud Azami |
| collection | DOAJ |
| description | In this article we study a coupled system for hyperbolic geometric
flow on a closed manifold M, with a harmonic flow map from M to
some closed target manifold N.
Then we show that this flow has a unique solution for a short-time.
After that, we find evolution equations for Riemannian curvature tensor,
Ricci curvature tensor, and scalar curvature of M under this flow.
In the final section we give some examples of this flow on closed manifolds. |
| first_indexed | 2024-12-23T21:19:46Z |
| format | Article |
| id | doaj.art-8bf5b6765f7242059f2361115b0ed843 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-23T21:19:46Z |
| publishDate | 2017-07-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-8bf5b6765f7242059f2361115b0ed8432022-12-21T17:30:48ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912017-07-012017165,19Harmonic-hyperbolic geometric flowShahroud Azami0 Imam Khomeini International Univ., Qazvin, Iran In this article we study a coupled system for hyperbolic geometric flow on a closed manifold M, with a harmonic flow map from M to some closed target manifold N. Then we show that this flow has a unique solution for a short-time. After that, we find evolution equations for Riemannian curvature tensor, Ricci curvature tensor, and scalar curvature of M under this flow. In the final section we give some examples of this flow on closed manifolds.http://ejde.math.txstate.edu/Volumes/2017/165/abstr.htmlHyperbolic geometric flowquasilinear hyperbolic equationstrict hyperbolicity |
| spellingShingle | Shahroud Azami Harmonic-hyperbolic geometric flow Electronic Journal of Differential Equations Hyperbolic geometric flow quasilinear hyperbolic equation strict hyperbolicity |
| title | Harmonic-hyperbolic geometric flow |
| title_full | Harmonic-hyperbolic geometric flow |
| title_fullStr | Harmonic-hyperbolic geometric flow |
| title_full_unstemmed | Harmonic-hyperbolic geometric flow |
| title_short | Harmonic-hyperbolic geometric flow |
| title_sort | harmonic hyperbolic geometric flow |
| topic | Hyperbolic geometric flow quasilinear hyperbolic equation strict hyperbolicity |
| url | http://ejde.math.txstate.edu/Volumes/2017/165/abstr.html |
| work_keys_str_mv | AT shahroudazami harmonichyperbolicgeometricflow |