Characterization of Finsler Space with Rander’s-Type Exponential-Form Metric
This study explores a unique Finsler space with a Rander’s-type exponential metric, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">G</mi><mrow><mo&g...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-03-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/7/1063 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850184664645369856 |
|---|---|
| author | Vinit Kumar Chaubey Brijesh Kumar Tripathi Sudhakar Kumar Chaubey Meraj Ali Khan |
| author_facet | Vinit Kumar Chaubey Brijesh Kumar Tripathi Sudhakar Kumar Chaubey Meraj Ali Khan |
| author_sort | Vinit Kumar Chaubey |
| collection | DOAJ |
| description | This study explores a unique Finsler space with a Rander’s-type exponential metric, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">G</mi><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><mi>α</mi><mo>+</mo><mi>β</mi><mo>)</mo></mrow><msup><mi>e</mi><mstyle scriptlevel="0" displaystyle="true"><mfrac><mi>β</mi><mrow><mo>(</mo><mi>α</mi><mo>+</mo><mi>β</mi><mo>)</mo></mrow></mfrac></mstyle></msup></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> is a Riemannian metric and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> is a 1-form. We analyze the conditions under which its hypersurfaces behave like hyperplanes of the first, second, and third kinds. Additionally, we examine the reducibility of the Cartan tensor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">C</mi></semantics></math></inline-formula> for these hypersurfaces, providing insights into their geometric structure. |
| format | Article |
| id | doaj-art-4abbbede78f347a58edc454cf53fe5d0 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-4abbbede78f347a58edc454cf53fe5d02025-08-20T02:17:00ZengMDPI AGMathematics2227-73902025-03-01137106310.3390/math13071063Characterization of Finsler Space with Rander’s-Type Exponential-Form MetricVinit Kumar Chaubey0Brijesh Kumar Tripathi1Sudhakar Kumar Chaubey2Meraj Ali Khan3Department of Mathematics, North-Eastern Hill University, Shillong 793022, IndiaDepartment of Mathematics, L. D. College of Engineering, Navrangpura, Ahmedabad 380015, IndiaSection of Mathematics, IT Department, University of Technology and Applied Sciences, P.O. Box 77, Shinas 324, OmanDepartment of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi ArabiaThis study explores a unique Finsler space with a Rander’s-type exponential metric, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">G</mi><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><mi>α</mi><mo>+</mo><mi>β</mi><mo>)</mo></mrow><msup><mi>e</mi><mstyle scriptlevel="0" displaystyle="true"><mfrac><mi>β</mi><mrow><mo>(</mo><mi>α</mi><mo>+</mo><mi>β</mi><mo>)</mo></mrow></mfrac></mstyle></msup></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> is a Riemannian metric and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> is a 1-form. We analyze the conditions under which its hypersurfaces behave like hyperplanes of the first, second, and third kinds. Additionally, we examine the reducibility of the Cartan tensor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">C</mi></semantics></math></inline-formula> for these hypersurfaces, providing insights into their geometric structure.https://www.mdpi.com/2227-7390/13/7/1063Finslerian hypersurfaceexponential (<i>α</i>, <i>β</i>)-metricCartan connectionhyperplane of first, second, and third kind |
| spellingShingle | Vinit Kumar Chaubey Brijesh Kumar Tripathi Sudhakar Kumar Chaubey Meraj Ali Khan Characterization of Finsler Space with Rander’s-Type Exponential-Form Metric Mathematics Finslerian hypersurface exponential (<i>α</i>, <i>β</i>)-metric Cartan connection hyperplane of first, second, and third kind |
| title | Characterization of Finsler Space with Rander’s-Type Exponential-Form Metric |
| title_full | Characterization of Finsler Space with Rander’s-Type Exponential-Form Metric |
| title_fullStr | Characterization of Finsler Space with Rander’s-Type Exponential-Form Metric |
| title_full_unstemmed | Characterization of Finsler Space with Rander’s-Type Exponential-Form Metric |
| title_short | Characterization of Finsler Space with Rander’s-Type Exponential-Form Metric |
| title_sort | characterization of finsler space with rander s type exponential form metric |
| topic | Finslerian hypersurface exponential (<i>α</i>, <i>β</i>)-metric Cartan connection hyperplane of first, second, and third kind |
| url | https://www.mdpi.com/2227-7390/13/7/1063 |
| work_keys_str_mv | AT vinitkumarchaubey characterizationoffinslerspacewithranderstypeexponentialformmetric AT brijeshkumartripathi characterizationoffinslerspacewithranderstypeexponentialformmetric AT sudhakarkumarchaubey characterizationoffinslerspacewithranderstypeexponentialformmetric AT merajalikhan characterizationoffinslerspacewithranderstypeexponentialformmetric |