Quasi-Einstein Kähler Metrics

We write an ansatz for quasi-Einstein Kähler metrics and construct new complete examples. Moreover, we construct new compact generalized quasi-Einstein Kähler metrics on some ruled surfaces, including some of Guan's examples as special cases.     

C-projective equivalence and integrability of the geodesic flow

We show that there is a deep relation between $C$-projective equivalence and Kähler–Liouville manifolds; the latter is a typical class of Kähler manifolds whose geodesic flows are integrable in Liouville’s sense.     

Mass mixing,the fourth generation,and the kinematic Higgs mechanism

We describe how to construct explicit chiral fermion mass terms using Dirac–Kähler (DK) spinors. Classical massive DK spinors are shown to be equivalent to four generations of Dirac spinors with equal mass coupled to a background U(2,2)$U(2,2)$ gauge field. Quantization breaks U(2,2)$U(2,2)$ to U(2)×U(2)$U(2)\times U(2)$, lifts mass spectrum degeneracy, and generates a non-trivial CKM mixing.     

K(a)hler Finsler Metrics Are Actually Strongly K(a)hler

In this paper,the K(a)hler conditions of the Chern-Finsler connection in complex Finsler geometry are studied,and it is proved that K(a)hler Finsler metrics are actually strongly K(a)hler.     

The Kodaira dimension of diffeomorphic Kähler threefolds

We provide infinitely many examples of pairs of diffeomorphic, non-simply-connected Kähler manifolds of complex dimension three with different Kodaira dimensions. Also, in any possible Kodaira dimension we find infinitely many pairs of non-deformation equivalent, diffeomorphic Kähler threefolds.

     

Kähler manifolds with homothetic foliation by curves

The aim of this paper is to classify compact, simply connected Kähler manifolds which admit totally geodesic, holomorphic complex homothetic foliations by curves.     

Derivations and the integral closure of ideals

Let be a complete local domain containing the rationals. Then there exists an integer such that for any ideal , if , , then there exists a derivation of with .

     

Generalized Elliptic Genus and Cobordism Class of Nonspin Real Grassmannians

We prove that Witten's generalized elliptic genusis rigid under certain group actions and constant(identically zero) on the real Grassmanniansr₄^2m+5, m 1, for appropriate vectorbundles.We also prove that all the Pontryagin numbers of theseGrassmannians are zero, i.e. they have cobordism class zero,which implies the vanishing of all genera.     

Exterior Difference System on Hypercubic Lattice

Based on the exterior differential calculus, we define the exterior difference system on the hypercubic lattice. The pairing formula, bracket, contract operator and Lie derivative operator for this system are also constructed. The discrete H. Cartan formulas are obtained too. After those preparations, we prove the discrete Frobenius Theorem, discrete retraction theorem and discrete Cartan–Kähler theorem.     

Angles in Complex Vector Spaces

The article reviews some of the (fairly scattered) information available in the mathematical literature on the subject of angles in complex vector spaces. The following angles and their relations are considered: Euclidean, complex, and Hermitian angles, (Kasner's) pseudo-angle, the Kähler angle (synonyms for the latter used in the literature are angle of inclination, characteristic deviation, holomorphic deviation, holomorphy angle, Wirtinger angle, slant angle).