Contact Geometry of Slant Submanifolds

This book contains an up-to-date survey and self-contained chapters on contact slant submanifolds and geometry, authored by internationally renowned researchers. The notion of slant submanifolds was introduced by Prof. B.Y. Chen in 1990, and A. Lotta extended this notion in the framework of contact geometry in 1996. Numerous differential geometers have since obtained interesting results on contact slant submanifolds. The book gathers a wide range of topics such as warped product semi-slant submanifolds, slant submersions, semi-slant - -, hemi-slant - -Riemannian submersions, quasi hemi-slant submanifolds, slant submanifolds of metric f-manifolds, slant lightlike submanifolds, geometric inequalities for slant submanifolds, 3-slant submanifolds, and semi-slant submanifolds of almost paracontact manifolds. The book also includes interesting results on slant curves and magnetic curves, where the latter represents trajectories moving on a Riemannian manifold under the action of magnetic field. It presents detailed information on the most recent advances in the area, making it of much value to scientists, educators and graduate students.

Auteur

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 d-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 awarded the 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. Professor Al-Solamy's research papers have been published in journals and conference proceedings of repute.

Contenu

General Properties of Slant Submanifolds in Contact Metric Manifolds.- Curvature Inequalities for Slant Submanifolds in Pointwise Kenmotsu Space Forms.- Some Basic Inequalities on Slant submanifolds in Space forms.- Geometry of Warped Product Semi-Slant Submanifolds in Almost Contact Metric Manifolds.- Slant and Semi Slant Submanifolds of Almost Contact and Paracontact Metric Manifolds.- The Slant Submanifolds in the Setting of Metric f-manifolds.- Slant, Semi-Slant and Pointwise Slant Submanifolds of 3-Structure Manifolds.- Slant Submanifolds of Conformal Sasakian Space Forms.- Slant Curves and Magnetic Curves.- Contact Slant Geometry of Submersions and Pointwise Slant and Semi-Slant Warped Product Submanifolds.