Quaternion Statistical Submanifolds and Submersions
This paper aims to develop a general theory of quaternion Kahlerian statistical manifolds and to study quaternion CR-statistical submanifolds in such ambient manifolds. It extends the existing theories of quaternion submanifolds and totally real submanifolds. Additionally, the work examines quaterni...
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MDPI AG
2024-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/1/53 |
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| author | Aliya Naaz Siddiqui Fatimah Alghamdi |
| author_facet | Aliya Naaz Siddiqui Fatimah Alghamdi |
| author_sort | Aliya Naaz Siddiqui |
| collection | DOAJ |
| description | This paper aims to develop a general theory of quaternion Kahlerian statistical manifolds and to study quaternion CR-statistical submanifolds in such ambient manifolds. It extends the existing theories of quaternion submanifolds and totally real submanifolds. Additionally, the work examines quaternion Kahlerian statistical submersions, including illustrative examples. The exploration also includes an analysis of the total space and fibers under certain conditions with example(s) in support. Moreover, Chen–Ricci inequality on the vertical distribution is derived for quaternion Kahlerian statistical submersions from quaternion Kahlerian statistical manifolds. |
| format | Article |
| id | doaj-art-8c79fe90099e41feb983ee59c2727860 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-8c79fe90099e41feb983ee59c27278602025-01-10T13:18:06ZengMDPI AGMathematics2227-73902024-12-011315310.3390/math13010053Quaternion Statistical Submanifolds and SubmersionsAliya Naaz Siddiqui0Fatimah Alghamdi1Division of Mathematics, School of Basic Sciences, Galgotias University, Greater Noida 203201, Uttar Pradesh, IndiaDepartment of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 21589, Saudi ArabiaThis paper aims to develop a general theory of quaternion Kahlerian statistical manifolds and to study quaternion CR-statistical submanifolds in such ambient manifolds. It extends the existing theories of quaternion submanifolds and totally real submanifolds. Additionally, the work examines quaternion Kahlerian statistical submersions, including illustrative examples. The exploration also includes an analysis of the total space and fibers under certain conditions with example(s) in support. Moreover, Chen–Ricci inequality on the vertical distribution is derived for quaternion Kahlerian statistical submersions from quaternion Kahlerian statistical manifolds.https://www.mdpi.com/2227-7390/13/1/53statistical manifoldsquaternion Kahlerian statistical manifoldsLagrangian submanifoldsquaternion CR-statistical submanifoldsstatistical submersionsquaternion Kahlerian statistical submersions |
| spellingShingle | Aliya Naaz Siddiqui Fatimah Alghamdi Quaternion Statistical Submanifolds and Submersions Mathematics statistical manifolds quaternion Kahlerian statistical manifolds Lagrangian submanifolds quaternion CR-statistical submanifolds statistical submersions quaternion Kahlerian statistical submersions |
| title | Quaternion Statistical Submanifolds and Submersions |
| title_full | Quaternion Statistical Submanifolds and Submersions |
| title_fullStr | Quaternion Statistical Submanifolds and Submersions |
| title_full_unstemmed | Quaternion Statistical Submanifolds and Submersions |
| title_short | Quaternion Statistical Submanifolds and Submersions |
| title_sort | quaternion statistical submanifolds and submersions |
| topic | statistical manifolds quaternion Kahlerian statistical manifolds Lagrangian submanifolds quaternion CR-statistical submanifolds statistical submersions quaternion Kahlerian statistical submersions |
| url | https://www.mdpi.com/2227-7390/13/1/53 |
| work_keys_str_mv | AT aliyanaazsiddiqui quaternionstatisticalsubmanifoldsandsubmersions AT fatimahalghamdi quaternionstatisticalsubmanifoldsandsubmersions |