Contact Forms in Geometry and Topology

Casorati Inequalities for Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature with Semi-Symmetric Metric Connection

“…Initiated by K. Kenmotsu in 1972 [ 23 ] as a branch of contact geometry, Kenmotsu geometry has generated a wide range of applications in physics (thermodynamics, classical mechanics, geometrical optics, geometric quantization, classical mechanics) and control theory [ 24 ]. The Kenmotsu statistical manifold , defined by H. Furuhata in [ 25 ], is obtained locally as a warped product between a holomorphic statistical manifold and a real line.…”

Curvature Invariants of Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature

“…Recently, Lee et al [20] studied optimal inequalities in terms of δ-Casorati curvatures of submanifolds in Kenmotsu space forms. We recall that the Kenmotsu geometry is an area of contact geometry initiated by Kenmotsu in [21], with many applications, e.g., in physics (geometrical optics, classical mechanics, thermodynamics, geometric quantization) and control theory [22]. This geometry arose in a natural way in the paper [21], where the author proposed to investigate the geometric properties of the warped product of the complex space with the real line.…”

“…This geometry arose in a natural way in the paper [21], where the author proposed to investigate the geometric properties of the warped product of the complex space with the real line. It is indeed a natural problem since this product is one of the three classes in Tanno's classification of connected almost contact Riemannian manifolds with an automorphism group of maximum dimension [22].…”

“…One reason to study the Kenmotsu manifolds is that this class of manifolds is one of the three classes in Tanno's classification of connected almost contact metric manifolds whose automorphism group has a maximum dimension. Another reason is that these manifolds are in some sense complementary to Sasaki manifolds: while some properties of Kenmotsu manifolds can be obtained deforming slowly properties of Sasaki manifolds, others are very different [22].…”