Zobrazeno 1 - 10
of 132
pro vyhledávání: '"BUCATARU, IOAN"'
Autor:
Bucataru, Ioan, Cretu, Georgeta
A strong Hamel function is a Hamel function that is the geodesic derivative of some 0-homogeneous function. We prove that strong Hamel functions induce dual symmetries and dynamical symmetries and provide the conditions such that these symmetries are
Externí odkaz:
http://arxiv.org/abs/2402.09791
Autor:
Bucataru, Ioan, Constantinescu, Oana
Publikováno v:
International Journal of Mathematics, Vol. 35, No. 06, 2450016 (2024)
We prove that various Finsler metrizability problems for sprays can be reformulated in terms of the geodesic invariance of two tensors (metric and angular). We show that gyroscopic sprays is the the largest class of sprays with geodesic invariant ang
Externí odkaz:
http://arxiv.org/abs/2303.14987
Publikováno v:
Annals of Global Analysis and Geometry, 62 (2022), no. 4, 815 - 827
We prove that in a Finsler manifold with vanishing $\chi$-curvature (in particular with constant flag curvature) some non-Riemannian geometric structures are geodesically invariant and hence they induce a set of non-Riemannian first integrals. Two al
Externí odkaz:
http://arxiv.org/abs/2204.05678
Autor:
Bucataru, Ioan
Publikováno v:
Proc. Amer. Math. Soc., vol. 150, no. 10, 2022, 4475--4486
Two geodesically (projectively) equivalent Finsler metrics determine a set of invariant volume forms on the projective sphere bundle. Their proportionality factors are geodesically invariant functions and hence they are first integrals. Being 0-homog
Externí odkaz:
http://arxiv.org/abs/2111.13374
Publikováno v:
Journal of Geometry and Physics Volume 166, August 2021, 104254
We use two non-Riemannian curvature tensors, the $\chi$-curvature and the mean Berwald curvature to characterise a class of Finsler metrics admitting first integrals.
Externí odkaz:
http://arxiv.org/abs/2101.11876
Autor:
Bucataru, Ioan, Fodor, Dan Gregorian
Publikováno v:
Beitrage zur Algebra und Geometrie / Contributions to Algebra and Geometry, 62(3), 2021, 745-754
In this paper we prove that a Finsler metrics has constant flag curvature if and only if the curvature of the induced nonlinear connection satisfies an algebraic identity with respect to some arbitrary second rank tensors. Such algebraic identity app
Externí odkaz:
http://arxiv.org/abs/1911.07476
Autor:
Bucataru, Ioan, Creţu, Georgeta
Publikováno v:
Publicationes Mathematicae Debrecen, 92 (3-4), 2020, 439-447
We present a new proof of a Finslerian version of Beltrami's theorem (1865) which works also in dimension 2.
Comment: 6 pages
Comment: 6 pages
Externí odkaz:
http://arxiv.org/abs/1902.05274
Autor:
Bucataru, Ioan, Creţu, Georgeta
Publikováno v:
The Journal of Geometric Analysis, January 2020, Volume 30, Issue 1, pp 617-631
We define a Weyl-type curvature tensor that provides a characterisation for Finsler metrics of constant flag curvature. When the Finsler metric reduces to a Riemannian metric, the Weyl-type curvature tensor reduces to the classic projective Weyl tens
Externí odkaz:
http://arxiv.org/abs/1808.05001
Publikováno v:
Differential Geometry and its Applications, Volume 56, February 2018, Pages 308-324
For a $2$-dimensional non-flat spray we associate a Berwald frame and a $3$-dimensional distribution that we call the Berwald distribution. The Frobenius integrability of the Berwald distribution characterises the Finsler metrizability of the given s
Externí odkaz:
http://arxiv.org/abs/1610.03949
Autor:
Bucataru, Ioan, Muzsnay, Zoltán
Publikováno v:
Comptes rendus - Math\'ematique 354 (2016), pp. 619-622
In his book "Differential Geometry of Spray and Finsler spaces", page 177, Zhongmin Shen asks "wether or not there always exist non-trivial Funk functions on a spray space". In this note, we will prove that the answer is negative for the geodesic spr
Externí odkaz:
http://arxiv.org/abs/1602.06734