This contributed volume includes chapters written by leading experts from around the world and provides a thorough and up-to-date exploration of geometric inequalities and their far-reaching applications. Covering a broad spectrum of topics, it discusses the intricacies of geometric solitons, generalized RicciYamabe solitons on three-dimensional Lie groups, and Riemannian invariants in submanifold theory. Readers will find in-depth discussions on B.Y. Chen inequalities for submanifolds of Kenmotsu space forms, refined ChenRicci inequalities for submersions from Sasakian space forms, and essential characterizations of perfect fluid and generalized RobertsonWalker space-times admitting k-almost RicciYamabe solitons. The book also investigates Riemannian concircular structure manifolds, statistical maps and their inequalities, as well as hyperbolic and -hyperbolic RicciYamabe solitons.
Chapter 1 Some inequalities for geometric solitons.
Chapter 2
Generalized Ricci-Yamabe Soliton On 3-Dimensional Lie Groups.
Chapter 3
Riemannian Invariants in Submanifold Theory.
Chapter 4 Chen Inequalities for
Submanifolds of Kenmotsu Space Forms.
Chapter 5 IMPROVED CHEN-RICCI
INEQUALITIES FOR SEMI-SLANT ^RIEMANNIAN SUBMERSIONS FROM SASAKIAN SPACE
FORMS.
Chapter 6 CHARACTERIZATIONS OF PERFECT FLUID AND GENERALIZED
ROBERTSON-WALKER SPACE-TIMES ADMITTING k ALMOST RICCI-YAMABE SOLITONS.-
Chapter 7 RIEMANNIAN CONCIRCULAR STRUCTURE MANIFOLDS AND SOLITONS.
Chapter
8 STATISTICAL MAPS AND A CHENS FIRST INEQUALITY FOR THESE MAPS.
Chapter 9
Hyperbolic Ricci-Yamabe Solitons and -Hyperbolic Ricci-Yamabe Solitons.-
Chapter 10 A survey on HitchinThorpe inequality and its extensions.
Chapter
11 The principal eigenvalue of a (p,q)-biharmonic system along the Ricci
flow.
Chapter 12 The Jacobi geometry of plane parametrized curves and
associated inequalities.
Chapter 13 B.-Y. Chen inequalities for submanifolds
of conformally flat manifolds.
Chapter 14 General Chen Inequalities for
Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant
-Sectional Curvature.
Chapter 15 B. Y. Chen inequalities for pointwise
quasi hemi-slant submanifolds of a Kaehler manifold.
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.
