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Geometry of Submanifolds and Applications

  • Book
  • © 2024

Overview

Editors:
  1. Bang-Yen Chen

    1. Department of Mathematics, Michigan State University, East Lansing, USA

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  2. Majid Ali Choudhary

    1. Department of Mathematics, Maulana Azad National Urdu University, Hyderabad, India

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    You can also search for this editor in PubMed   Google Scholar

  3. Mohammad Nazrul Islam Khan

    1. Department of Computer Engineering, Qassim University, College of Computer, Buraydah, Saudi Arabia

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  • Discusses a wide range of topics in geometry of submanifolds
  • Includes numerous problems and conjectures on submanifolds, providing insights for scientists and graduate students
  • Showcases the latest findings on Pythagorean submanifolds and submanifolds of four-dimensional f-manifolds

Part of the book series: Infosys Science Foundation Series (ISFS)

Part of the book sub series: Infosys Science Foundation Series in Mathematical Sciences (ISFM)

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About this book

This book features chapters written by renowned scientists from various parts of the world, providing an up-to-date survey of submanifold theory, spanning diverse topics and applications. The book covers a wide range of topics such as Chen–Ricci inequalities in differential geometry, optimal inequalities for Casorati curvatures in quaternion geometry, conformal η-Ricci–Yamabe solitons, submersion on statistical metallic structure, solitons in f(R, T)-gravity, metric-affine geometry, generalized Wintgen inequalities, tangent bundles, and Lagrangian submanifolds.


Moreover, the book showcases the latest findings on Pythagorean submanifolds and submanifolds of four-dimensional f-manifolds. The chapters in this book delve into numerous problems and conjectures on submanifolds, providing valuable insights for scientists, educators, and graduate students looking to stay updated with the latest developments in the field. With its comprehensive coverage and detailed explanations, this book is an essential resource for anyone interested in submanifold theory.

Keywords

Table of contents (13 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Recent Developments on Chen–Ricci Inequalities in Differential Geometry

    • Bang-Yen Chen, Adara M. Blaga
    Pages 1-61

  3. Solitons in \(f(\mathcal {R},T)\)-Gravity

    • Uday Chand De, Krishnendu De
    Pages 63-77

  4. A Survey on Lagrangian Submanifolds of Nearly Kaehler Six-Sphere

    • Ramesh Sharma
    Pages 79-88

  5. Pythagorean Submanifolds

    • Muhittin Evren Aydın, Adela Mihai, Cihan Özgür
    Pages 89-98

  6. On 4-Dimensional Submanifolds of f-Manifolds

    • Gherici Beldjilali
    Pages 99-117

  7. Almost Yamabe Solitons on a Total Space of Almost Hermitian Submersions

    • Tanveer Fatima, Mehmet Akif Akyol, Rakesh Kumar
    Pages 119-132

  8. Generalized Wintgen Inequalities for \((\epsilon )\)-Para Sasakian Manifold

    • Majid Ali Choudhary, Lovejoy S. Das, Mohd. Danish Siddiqi, Oğuzhan Bahadır
    Pages 133-145

  9. Certain Optimal Inequalities for Casorati Curvatures in Quaternion Geometry

    • Mohd Danish Siddiqi, Aliya Naaz Siddiqui, Kamran Ahmad
    Pages 147-158

  10. Gravity and Dark Matter in the Framework of Metric-Affine Geometry

    • Ghodratallah Fasihi-Ramandi, Vahid Pirhadi
    Pages 159-168

  11. Submersion on Statistical Metallic Structure

    • Mohit Saxena
    Pages 169-180

  12. Tangent Bundles Endowed with Quarter-Symmetric Non-metric \(\xi \)-Connection on 3-Dimensional Quasi-Sasakian Manifolds

    • Mohammad Nazrul Islam Khan, Ljubica Velimirović
    Pages 181-196

  13. The Darboux Mate and the Higher Order Curvatures of Spherical Legendre Curves

    • Mircea Crasmareanu
    Pages 197-207

  14. Conformal \(\eta \)-Ricci-Yamabe Solitons in the Framework of Riemannian Manifolds

    • Sudhakar Kumar Chaubey, Abdul Haseeb
    Pages 209-224
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Editors and Affiliations

  • Department of Mathematics, Michigan State University, East Lansing, USA

    Bang-Yen Chen

  • Department of Mathematics, Maulana Azad National Urdu University, Hyderabad, India

    Majid Ali Choudhary

  • Department of Computer Engineering, Qassim University, College of Computer, Buraydah, Saudi Arabia

    Mohammad Nazrul Islam Khan

About the editors

Bang-Yen Chen, a Taiwanese–American mathematician, is University Distinguished Professor Emeritus at Michigan State University, USA, since 2012. He completed his Ph.D. degree at the University of Notre Dame, USA, in 1970, under the supervision of Prof. Tadashi Nagano. He received his M.Sc. degree from National Tsing Hua University, Hsinchu, Taiwan, in 1967, and B.Sc. degree from Tamkang University, Taipei, Taiwan, in 1965. Earlier at Michigan State University, he served as University Distinguished Professor (1990–2012), Full Professor (1976), Associate Professor (1972), and Research Associate (1970–1972). He taught at Tamkang University, Taiwan, from 1966 to 1968, and at National Tsing Hua University, Taiwan, during the academic year 1967–1968.


Majid Ali Choudhary is Assistant Professor at the Department of Mathematics at Maulana Azad National Urdu University, Hyderabad, India. In 2014, he received his Ph.D. in Mathematics from Jamia MilliaIslamia, India, under the supervision of Prof. Mohammad Hasan Shahid. He was awarded the DST, Government of India’s Inspire Fellowship to pursue a Ph.D. degree. His M.Sc. degree from Jamia Millia Islamia, New Delhi, India, was conferred to him in 2008, and he also won a Gold Medal for securing the first position in the University. His areas of interest include Ricci solitons, Chen–Ricci inequalities, Wintgen inequalities, and inequalities involving Casorati curvatures. He also studies the geometry of submanifolds in Riemannian and semi-Riemannian manifolds. Research publications of him have been appearing in journals of repute.


Mohammad Nazrul Islam Khan is Associate Professor at the Department of Computer Engineering, College of Computer, Qassim University, Saudi Arabia, since 2011. He completed his Ph. D. degree at the University of Lucknow, India, in 2001, under the supervision of Prof. Ram Nivas. He received his M.Sc. degree from the University of Lucknow, India, in 1997. Earlier, he served at Salalah College of Technology, Salalah, Oman, from 2009 to 2011. He taught at Azad Institute of Engineering and Technology, Lucknow, India, as Assistant Professor (2003–2009) and Lecturer (2001–2003) and at Amiruddaula Islamia Degree College, Lucknow, from 1997 to 2001. He has published more than 60 research articles in various national and international journals of repute.

Bibliographic Information

  • Book Title: Geometry of Submanifolds and Applications

  • Editors: Bang-Yen Chen, Majid Ali Choudhary, Mohammad Nazrul Islam Khan

  • Series Title: Infosys Science Foundation Series

  • DOI: https://doi.org/10.1007/978-981-99-9750-3

  • Publisher: Springer Singapore

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024

  • Hardcover ISBN: 978-981-99-9749-7Published: 27 March 2024

  • Softcover ISBN: 978-981-99-9752-7Published: 27 March 2025

  • eBook ISBN: 978-981-99-9750-3Published: 26 March 2024

  • Series ISSN: 2363-6149

  • Series E-ISSN: 2363-6157

  • Edition Number: 1

  • Number of Pages: X, 224

  • Number of Illustrations: 2 b/w illustrations, 3 illustrations in colour

  • Topics: Differential Geometry, Global Analysis and Analysis on Manifolds

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