共查询到10条相似文献,搜索用时 46 毫秒
1.
Marija S. ?iri? Milan Lj. Zlatanovi? Mi?a S. Stankovi? Ljubica S. Velimirovi? 《Applied mathematics and computation》2012,218(12):6648-6655
In this paper geodesic mappings of equidistant generalized Riemannian spaces are discussed. It is proved that each equidistant generalized Riemannian space of basic type admits non-trivial geodesic mapping with preserved equidistant congruence. Especially, there exists non-trivial geodesic mapping of equidistant generalized Riemannian space onto equidistant Riemannian space. An example of geodesic mapping of an equidistant generalized Riemannian spaces is presented. 相似文献
2.
Envelopes of splines in the projective plane 总被引:2,自引:0,他引:2
In this paper a family of curvesRiemannian cubicsinthe unit sphere and the real projective plane is investigated.Riemannian cubics naturally arise as solutions to variationalproblems in Riemannian spaces. It is remarkable to find thatan envelope of lines generated by a Riemannian cubic in onespace is (nearly) a Riemannian cubic in another space. 相似文献
3.
Lyle Noakes 《Advances in Computational Mathematics》2002,17(4):385-395
Riemannian quadratics are C
1 curves on Riemannian manifolds, obtained by performing the quadratic recursive deCastlejeau algorithm in a Riemannian setting. They are of interest for interpolation problems in Riemannian manifolds, such as trajectory-planning for rigid body motion. Some interpolation properties of Riemannian quadratics are analysed when the ambient manifold is a sphere or projective space, with the usual Riemannian metrics. 相似文献
4.
Riemannian cubics are curves that generalise cubic polynomials to arbitrary Riemannian manifolds, in the same way that geodesics generalise straight lines. Considering that geodesics can be extended indefinitely in any complete manifold, we ask whether Riemannian cubics can also be extended indefinitely. We find that there are always exceptions in Riemannian manifolds with strictly negative sectional curvature. On the other hand, we show that Riemannian cubics can always be extended in complete locally symmetric Riemannian manifolds of non-negative curvature. 相似文献
5.
Mohamed Boucetta 《Journal of the Egyptian Mathematical Society》2011,19(1-2):57-70
We introduce Riemannian Lie algebroids as a generalization of Riemannian manifolds and we show that most of the classical tools and results known in Riemannian geometry can be stated in this setting. We give also some new results on the integrability of Riemannian Lie algebroids. 相似文献
6.
Bayram Ṣahin 《Indagationes Mathematicae》2012,23(1-2):80-94
We construct Gauss–Weingarten-like formulas and define O’Neill’s tensors for Riemannian maps between Riemannian manifolds. By using these new formulas, we obtain necessary and sufficient conditions for Riemannian maps to be totally geodesic. Then we introduce semi-invariant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds, give examples and investigate the geometry of leaves of the distributions defined by such maps. We also obtain necessary and sufficient conditions for semi-invariant maps to be totally geodesic and find decomposition theorems for the total manifold. Finally, we give a classification result for semi-invariant Riemannian maps with totally umbilical fibers. 相似文献
7.
Bayram Ṣahin 《Central European Journal of Mathematics》2010,8(3):437-447
We introduce anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give an example,
investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity
of such submersions. We also find necessary and sufficient conditions for a Langrangian Riemannian submersion, a special anti-invariant
Riemannian submersion, to be totally geodesic. Moreover, we obtain decomposition theorems for the total manifold of such submersions. 相似文献
8.
A Riemannian orbifold is a mildly singular generalization of a Riemannian manifold which is locally modeled on the quotient of a connected, open manifold under a finite group of isometries. If all of the isometries used to define the local structures of an entire orbifold are orientation preserving, we call the orbifold locally orientable. We use heat invariants to show that a Riemannian orbifold which is locally orientable cannot be Laplace isospectral to a Riemannian orbifold which is not locally orientable. As a corollary we observe that a Riemannian orbifold that is not locally orientable cannot be Laplace isospectral to a Riemannian manifold. 相似文献
9.
We show that certain right-invariant metrics endow the
infinite-dimensional Lie group of all smooth
orientation-preserving diffeomorphisms of the circle with a
Riemannian structure. The study of the Riemannian exponential map
allows us to prove infinite-dimensional counterparts of results
from classical Riemannian geometry: the Riemannian exponential map is
a smooth local diffeomorphism and the length-minimizing property of
the geodesics holds. 相似文献
10.
Marcos M. Alexandrino 《Geometriae Dedicata》2004,108(1):141-152
A map of a Riemannian manifold into an euclidian space is said to be transnormal if its restrictions to neighbourhoods of
regular level sets are integrable Riemannian submersions. Analytic transnormal maps can be used to describe isoparametric
submanifolds in spaces of constant curvature and equifocal submanifolds with flat sections in simply connected symmetric spaces.
These submanifolds are also regular leaves of singular Riemannian foliations with sections. We prove that regular level sets
of an analytic transnormal map on a real analytic complete Riemannian manifold are equifocal submanifolds and leaves of a
singular Riemannian foliation with sections. 相似文献