λ-Projectively Related Finsler Metrics and Finslerian Projective Invariants
Introduction In this paper, by using the concept of spherically symmetric Finsler metric, we define the notion of -projectively related metrics as an extension of projectively related metrics. We construct some non-trivial examples of -projectively related metrics. Let F and be two -projectivel...
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| Format: | Article |
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Kharazmi University
2020-12-01
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| Series: | پژوهشهای ریاضی |
| Subjects: | |
| Online Access: | http://mmr.khu.ac.ir/article-1-2868-en.html |
| _version_ | 1797871642154631168 |
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| author | Akbar Tayebi Morad Bahadori Hassan Sadeghi |
| author_facet | Akbar Tayebi Morad Bahadori Hassan Sadeghi |
| author_sort | Akbar Tayebi |
| collection | DOAJ |
| description | Introduction
In this paper, by using the concept of spherically symmetric Finsler metric, we define the notion of -projectively related metrics as an extension of projectively related metrics. We construct some non-trivial examples of -projectively related metrics. Let F and be two -projectively related metrics on a manifold M. We find the relation between the geodesics of F and and prove that any geodesic of F is a multiple of a geodesic of and the other way around. There are several projective invariants of Finsler metrics, namely, Douglas metrics, Weyl metrics and generalized Douglas-Weyl curvature. We prove that the Douglas metrics, Weyl metrics and generalized Douglas-Weyl metrics are -projective invariants.
Material and methods
First we obtain the spray coefficients of a spherically symmetric Finsler metric. By considering it, we define -projectively related metrics which is a generalization of projectively related Finsler metrics. Then we find the geodesics of two -projectively related metrics. We obtain the relation between Douglas, Weyl and generalized Douglas-Weyl curvatures of two -projectively related metrics.
Results and discussion
We find the Douglas curvature, Weyl curvature and generalized Douglas-Weyl curvature of two -projectively related Finsler metrics. These calculations tell us that these class of Finsler metrics are -projective invariants.
Conclusion
The following conclusions were drawn from this research.
We prove that the Douglas curvature, Weyl curvature and generalized Douglas-Weyl curvature are -projective invariants.
Let F and be two -projectively related metrics on a manifold M. We show that F is a Berwald metric if and only if is a Berwald metric. ./files/site1/files/64/12.pdf |
| first_indexed | 2024-04-10T00:47:04Z |
| format | Article |
| id | doaj.art-4caa516fa1a64bec92d3378feb70c2a8 |
| institution | Directory Open Access Journal |
| issn | 2588-2546 2588-2554 |
| language | fas |
| last_indexed | 2024-04-10T00:47:04Z |
| publishDate | 2020-12-01 |
| publisher | Kharazmi University |
| record_format | Article |
| series | پژوهشهای ریاضی |
| spelling | doaj.art-4caa516fa1a64bec92d3378feb70c2a82023-03-13T19:22:24ZfasKharazmi Universityپژوهشهای ریاضی2588-25462588-25542020-12-0164621630λ-Projectively Related Finsler Metrics and Finslerian Projective InvariantsAkbar Tayebi0Morad Bahadori1Hassan Sadeghi2 University of Qom University of Qom University of Qom Introduction In this paper, by using the concept of spherically symmetric Finsler metric, we define the notion of -projectively related metrics as an extension of projectively related metrics. We construct some non-trivial examples of -projectively related metrics. Let F and be two -projectively related metrics on a manifold M. We find the relation between the geodesics of F and and prove that any geodesic of F is a multiple of a geodesic of and the other way around. There are several projective invariants of Finsler metrics, namely, Douglas metrics, Weyl metrics and generalized Douglas-Weyl curvature. We prove that the Douglas metrics, Weyl metrics and generalized Douglas-Weyl metrics are -projective invariants. Material and methods First we obtain the spray coefficients of a spherically symmetric Finsler metric. By considering it, we define -projectively related metrics which is a generalization of projectively related Finsler metrics. Then we find the geodesics of two -projectively related metrics. We obtain the relation between Douglas, Weyl and generalized Douglas-Weyl curvatures of two -projectively related metrics. Results and discussion We find the Douglas curvature, Weyl curvature and generalized Douglas-Weyl curvature of two -projectively related Finsler metrics. These calculations tell us that these class of Finsler metrics are -projective invariants. Conclusion The following conclusions were drawn from this research. We prove that the Douglas curvature, Weyl curvature and generalized Douglas-Weyl curvature are -projective invariants. Let F and be two -projectively related metrics on a manifold M. We show that F is a Berwald metric if and only if is a Berwald metric. ./files/site1/files/64/12.pdfhttp://mmr.khu.ac.ir/article-1-2868-en.htmlprojective invariantprojectively flat metricprojectively related metricsdouglas metricweyl metricgeneralized douglas-weyl metric. |
| spellingShingle | Akbar Tayebi Morad Bahadori Hassan Sadeghi λ-Projectively Related Finsler Metrics and Finslerian Projective Invariants پژوهشهای ریاضی projective invariant projectively flat metric projectively related metrics douglas metric weyl metric generalized douglas-weyl metric. |
| title | λ-Projectively Related Finsler Metrics and Finslerian Projective Invariants |
| title_full | λ-Projectively Related Finsler Metrics and Finslerian Projective Invariants |
| title_fullStr | λ-Projectively Related Finsler Metrics and Finslerian Projective Invariants |
| title_full_unstemmed | λ-Projectively Related Finsler Metrics and Finslerian Projective Invariants |
| title_short | λ-Projectively Related Finsler Metrics and Finslerian Projective Invariants |
| title_sort | λ projectively related finsler metrics and finslerian projective invariants |
| topic | projective invariant projectively flat metric projectively related metrics douglas metric weyl metric generalized douglas-weyl metric. |
| url | http://mmr.khu.ac.ir/article-1-2868-en.html |
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