共查询到20条相似文献,搜索用时 15 毫秒
1.
Walter Benz 《Journal of Geometry》2004,79(1-2):27-30
This paper is concerned with the characterization of area-preserving mappings
of real inner product spaces. 相似文献
2.
Walter Benz Hamburg 《Journal of Geometry》2001,70(1-2):8-16
Suppose that X is the set of points of a hyperbolic geometry of finite or infinite dimension , and that is a fixed real number and N>1 a fixed integer. Let be a mapping such that for every if h(x, y)=, then h(f,(x),f,(y)) , and if h(x,y) = N, then h(f,(x),f,(y)) , where h,(p,q) designates the hyperbolic distance of p,q
. Then f is an isometry of X. Note that there is no regularity assumption on f, like continuity or even differentiability. Moreover, we present an example showing that the assumption that one fixed distance
> 0 is preserved does not characterize hyperbolic isometries.
Received 17 February 2000. 相似文献
3.
V. Pambuccian 《Acta Mathematica Hungarica》2003,100(1-2):63-67
Positive Lω1ω definitions of point-inequality and noncollinearity in terms of collinearity, which are valid in plane hyperbolic geometry over arbitrary Archimedean ordered Euclidean fields, provide a synthetic proof of the theorem stated in the title and first noticed to be a corollary of a result from [2] by R. Höfer [3]. 相似文献
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Rui Hu 《Journal of Mathematical Analysis and Applications》2008,343(2):1161-1165
In this paper, in connection with the known result of Baker and Vogt, we get if preserves equality of distance with dimension X?2 and Y is strictly convex, the range of f contains a segment, then f is affine. 相似文献
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Tatjana Petek 《Linear and Multilinear Algebra》2013,61(7):903-925
We obtain a general form of a surjective (not assumed additive) mapping φ, preserving the nonzero idempotency of a certain product, being defined (a) on the algebra of all bounded linear operators B(X), where X is at least three-dimensional real or complex Banach space, (b) on the set of all rank-one idempotents in B(X) and (c) on the set of all idempotents in B(X). In any of the cases it turns out that φ is additive and either multiplicative or antimultiplicative. 相似文献
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Jor-Ting Chan Chi-Kwong Li Nung-Sing Sze 《Proceedings of the American Mathematical Society》2007,135(4):977-986
Let be the set of complex matrices, and for every , let denote the spectrum of . For various types of products on , it is shown that a mapping satisfying for all has the form for some invertible and scalar . The result covers the special cases of the usual product , the Jordan triple product , and the Jordan product . Similar results are obtained for Hermitian matrices.
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Péter T. Nagy 《Geometriae Dedicata》1991,37(2):125-139
This paper is devoted to the investigation of the geometry of left invariant metrics on the isometry group of the hyperbolic plane determined by the kinetic energy of a rigid particle system.Dedicated to the memory of Professor A. M. Vasil'ev (1923–1987) 相似文献
15.
The first author introduced a Riemannian invariant denoted by δ and proved in [4] that everyn-dimensional submanifold of the complex hyperbolicm-space ℂH
m
(4c) of constant holomorphic sectional curvature 4c<0 satisfies a basic inequality
, whereH
2 denotes the squared mean curvature of the submanifold. The main purpose of this paper is to completely classify properCR-submanifolds of complex hyperbolic spaces which satisfy the equality case of this inequality.
Dedicated to Leopold Verstraelen on his fiftieth birthday 相似文献
16.
Katrin Gelfert 《Mathematische Zeitschrift》2009,261(4):711-724
For a diffeomorphism which preserves a hyperbolic measure the potential is studied. Various types of pressure of are introduced. It is shown that these pressures satisfy a corresponding variational principle.
This research was supported by the grant EU FP6 ToK SPADE2. The author is grateful to IM PAN Warsaw for the hospitality and
to C. Wolf for discussions about suitable concepts of pressure. 相似文献
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S. Sh. Kozhegel’dinov 《Mathematical Notes》2010,88(5-6):696-700
We study the properties of pairs of triangles with integer sides whose common area is the square of a natural number. 相似文献
19.
Manabu Ito 《复变函数与椭圆型方程》2015,60(11):1612-1619
It is the purpose of this paper to supplement our previous work concerning upper estimates for hyperbolic metrics on subdomains. Specifically, our interest is in determining when equality holds in the relevant inequality to clarify the situation that has failed to be explicitly mentioned before. The method of proof again involves a standard technique based on the classical Schwarz–Pick lemma. 相似文献