ON SOLVABLE COMPLETE LIE SUPERALGEBRAS

The authors discuss the properties of solvable complete Lie superalgebra, proving that solvable Lie superalgebras of maximal rank are complete.     

THE NEARLY K¨AHLER STRUCTURE AND MINIMAL SURFACES IN S~6

ＴＨＥＮＥＡＲＬＹＫ¨ＡＨＬＥＲＳＴＲＵＣＴＵＲＥＡＮＤＭＩＮＩＭＡＬＳＵＲＦＡＣＥＳＩＮＳ６ＳＨＥＮＹＩＢＩＮＧＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＦｅｂｒｕａｒｙ１１，１９９５．ＲｅｖｉｓｅｄＯｃｔｏｂｅｒ１７，１９９６．Ｄｅｐａｒｔｍｅ...     

A Weierstrass type representation for minimal surfaces in Sol

The normal Gauss map of a minimal surface in the model space of solvegeometry is a harmonic map with respect to a certain singular Riemannian metric on the extended complex plane.

     

THE NEARLY K\"AHLER STRUCTURE AND MINIMAL SURFACES IN S^6

In terms of the almost complex connection and the unitary moving frame,a complex version on the theory of the nearly Kaehler structure in S^6 is given.Under this framework, minimal surfaces in the nearly Kaehler,S^6 are studied.A complete classification for complete minimal surfaces in S^6 with constant,Kaehler angle and nonnegative curvature is given.Moreover,almost complex curves in S^6 are considered.     

三维Minkowski空间中的曲面及其可积性

利用可积系统的思想,借助三维Minkowski空间L3的矩阵模型,研究了L3中具有调和逆平均曲率的类空曲面和洛伦兹调和逆平均曲率类时曲面的可积性及其形变.     

REPRESENTATIONS OF SOLVABLE LIE GROUPS AND GEOMETRIC QUANTIZATION

1.IntroductionTheorbitmetheodpresentedbyKirillovandKostanthajsgreatlybeendevelopedrecentlytorealizerepresentationsofgroups(finiteandinfinite-dimensionalgroups).Italsohascloserelationshipswiththeclassificationofrepresentationsl'].Infact,thedeeporiginoftheorbitmetheodisgeometricquantization.Theproblemofgeometricquantizationis,startingfromthegeometryofasymplecticmanifold(M,w)whichgivesthemodelofaclassicalmechenicalsystem,toconstructaHilbertspaceHandasetofoperatorsonitwhichgivethequantumanalogue…     

无限的可解SD3—群

设Ｇ是个无限的多重循环群，若Ｇ的任意指数有限的真子群都是３元生成的，则Ｇ＾（６）＝１，且Ｇ也是３元生成的。     

Harmonic morphisms from the classical compact semisimple Lie groups

In this article, we introduce a new method for manufacturing harmonic morphisms from semi-Riemannian manifolds. This is employed to yield a variety of new examples from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with their standard Riemannian metrics. We develop a duality principle and show how this can be used to construct the first known examples of harmonic morphisms from the non-compact Lie groups , SU ^*(2n), , SO ^*(2n), SO(p, q), SU(p, q) and Sp(p, q) equipped with their standard dual semi-Riemannian metrics.      

DEGENERATIONS OF 7-DIMENSIONAL NILPOTENT LIE ALGEBRAS

ABSTRACT

We study the varieties of Lie algebra laws and their subvarieties of nilpotent Lie algebra laws. We classify all degenerations of (almost all) five-step and six-step nilpotent seven-dimensional complex Lie algebras. One of the main tools is the use of trivial and adjoint cohomology of these algebras. In addition, we give some new results on the varieties of complex Lie algebra laws in low dimension.     

DERIVED LENGTHS OF SOLVABLE GROUPS SATISFYING THE ONE-PRIME HYPOTHESIS. III

Abstract

The purpose of this paper is to extend the result in Park (Park, J. (2001). Birational maps of del Pezzo fibrations. J. Reine Angew. Math. 538:213–221) in the case of del Pezzo fibrations of degree 1. To this end we investigate the anticanonical linear systems of del Pezzo surfaces of degree 1. We then classify all possible effective anticanonical divisors on Gorenstein del Pezzo surfaces of degree 1 with canonical singularities.