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 ChenRicci inequalities in differential geometry, optimal inequalities for Casorati curvatures in quaternion geometry, conformal -RicciYamabe 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.

Bang-Yen Chen, a TaiwaneseAmerican 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 (19902012), Full Professor (1976), Associate Professor (1972), and Research Associate (19701972). He taught at Tamkang University, Taiwan, from 1966 to 1968, and at National Tsing Hua University, Taiwan, during the academic year 19671968.
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 Indias 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, ChenRicci 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 (20032009) and Lecturer (20012003) 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.

Chapter 1 Recent Developments on ChenRicci Inequalities in Differential Geometry.- Chapter 2 Solitons in F(R, T)-Gravity.- Chapter 3 A Survey on Lagrangian Submanifolds of Nearly Kaehler 6-Sphere.- Chapter 4 Pythagorean Submanifolds.- Chapter .5 On 4-Dimensional Submanifolds of F-Manifolds