Complex Geometry of Slant Submanifolds

Bang-Yen Chen, a Taiwanese-American mathematician, is 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.He is responsible for the invention of δ-invariants (also known as Chen invariants), Chen inequalities, Chen conjectures, development of the theory of submanifolds of finite type, and co-developed (M+, M–)-theory. An author of 12 books and more than 500 research articles, Prof. Chen has been Visiting Professor at various universities, including the University of Notre Dame, USA; Science University of Tokyo, Japan; the University of Lyon, France; Katholieke Universiteit Leuven, Belgium; the University of Rome, Italy; National Tsing Hua University, Taiwan; and Tokyo Denki University, Japan. Mohammad Hasan Shahid is Professor at the Department of Mathematics, Jamia Millia Islamia, New Delhi, India. He earned his Ph.D. in Mathematics from Aligarh Muslim University, India, on the topic “On geometry of submanifolds” in 1988 under (Late) Prof. Izhar Husain. Earlier, he served as Associate Professor at King Abdul Aziz University, Jeddah, Saudi Arabia, from 2001 to 2006. He was a recipient of the postdoctoral fellowship from the University of Patras, Greece, from October 1997 to April 1998. He has published more than 100 research articles in various national and international journals of repute. Recently, he was awardedthe Sultana Nahar Distinguished Teacher award of the Year 2017–2018 for his outstanding contribution to research. For research works and delivering talks, Prof. Shahid has visited several universities of the world: the University of Leeds, UK; the University of Montpellier, France; the University of Sevilla, Spain; Hokkaido University, Japan; Chuo University, Japan; and Manisa Celal Bayar University, Turkey.Falleh Al-solamy is President at King Khalid University, Abha, Saudi Arabia. Earlier, he was Professor of Differential Geometry at King Abdulaziz University, Jeddah, Saudi Arabia. He studied Mathematics at King Abdulaziz University, Jeddah, Saudi Arabia, and earned his Ph.D. in Mathematics from the University of Wales Swansea, Swansea, UK, in 1998, under Prof. Edwin Beggs. His research interests concern the study of the geometry of submanifolds in Riemannian and semi-Riemannian manifolds, Einstein manifolds, and applications of differential geometry in physics. ProfessorAl-Solamy’s research papers have been published in journals and conference proceedings of repute.

“As a global view, one must mention that many of the presented results in the above contributions are given with their complete proofs; this fact increases the value of the book and makes it excellent scientific material for the researchers in the field. Besides the high level and the valuable contents of the book, one must remark that the topic is of high interest for the specialists in differential geometry.” (Adela-Gabriela Mihai, zbMATH 1511.53002, 2023)

• An Overview of Recent Developments of Slant Submanifolds.- Slant Surfaces in Complex Space Forms.- Slant Geometry of Warped products in Kaehler and Nearly Kaehler Manifolds.- Slant Geometry of Riemannian Submersions from Almost Hermitian Manifolds.- Slant Submanifolds of the nearly Kaehler 6-sphere.- Slant submanifolds of para Hermitian manifolds.- Hemi-slant and Semi-slant Submanifolds in locally conformal Kaehler Manifolds.- Slant Submanifolds and Their Warped Product in Locally Product Riemannian Manifolds.- Slant Submanifolds of Quaternion Kaehler and Hyper-Kaehler Manifolds.- Geometry of Pointwise Slant Immersions in Almost Hermitian Manifolds.