Current developments in differential geometry and its related fields : proceedings of the 4th International Colloquium on Differential Geometry and its Related Fields, Veliko Tarnovo, Bulgaria, 8-12 September 2014 - Adachi, Toshiaki; Hashimoto, Hideya; Hristov, Milen J. (World Scientific, 2016)
This volume contains contributions by the main participants of the 4th International Colloquium on Differential Geometry and its Related Fields (ICDG2014). These articles cover recent developments and are devoted mainly to the study of some geometric structures on manifolds and graphs. Readers will find a broad overview of differential geometry and its relationship to other fields in mathematics and physics.Contents:PrefaceOrganizing and Scientific Advisory CommitteesPresentationsEinstein Metrics on the Symplectic Group Which are Not Naturally Reductive (Andreas Arvanitoyeorgos, Yusuke Sakane and Marina Statha)Laplacians for Finite Regular Kähler Graphs and for Their Dual Graphs (Toshiaki Adachi)S1-Invariant Einstein-Weyl Structure and Twistor Correspondence (Fuminori Nakata)A Family of Surfaces in E3 Given by an Over-Determined System (Naoya Ando)Some Remarks on Noncommutative Instantons (Nikolay A Ivanov)Almost CR Structure on the Twistor Space of a Quaternionic CR Manifold (Hiroyuki Kamada and Shin Nayatani)Five Dimensional Lie Groups Which are Almost Contact B-Metric Manifolds with Three Natural Connections (Miroslava Ivanova and Hristo Manev)On Hyperelliptic Minimal Surfaces with Even Genus (Norio Ejiri and Toshihiro Shoda)Laplacians of Kähler Graphs (Yaermaimaiti Tuerxunmaimaiti (Yarmamat Tursun))Hopf Fibration and Cartan Imbedding of Type AI (Hideya Hashimoto and Kazuhiro Suzuki)On Totally Umbilical and Screen Totally Umbilical Radical Transversal Lightlike Hypersurfaces of Kähler-Norden Manifolds (Galia Nakova)Complex Statistical Manifolds and Complex Affine Immersions (Hiroshi Matsuzoe)A Method of Determining the SO(7)-Invariants for Curves in Im O by Their G2-Invariants (Misa Ohashi)Magnetic Jacobi Fields for Surface Magnetic Fields (Qingsong Shi)A Geometric Study on Laplace Transformed Curves (Milen J Hristov)Vector-Valued Laplace Transformation Applied to Rational Bézier Curves (Milen J Hristov)Readership: Professionals, researchers and graduate students in differential geometry, complex analysis, probability theory and mathematical physics.Keywords:Einstein Metrics on Lie Groups;Einstein-Weyl Structures;Quaternionic CR Manifolds;Exceptional Geometry;Totally Geodesic Surfaces in Symmetric Spaces;Mathematical Physics;Lightlike Submanifolds;Complex Statistical Manifolds;New Treatment of Surfaces in a Euclidean 3-Space;Laplacians on GraphsKey Features:Consists of original papers and some announcements on recent developments in differential geometry and related fieldsNew understanding on geometric structures on manifolds and their discretized objectsA good guide for young scientists studying in this field.