List of papers on geometry :
Updated December 16, 2008
- Rylov Yu. A. (2008) Some subtleties of
Riemannian geometry Available at http://arXiv.org/abs/0812.2833
- Rylov Yu. A. (2008) Generalization of
relativistic particle dynamics on the case of non-Riemannian space-time
geometry Available at http://arXiv.org/abs/0811.4562
- Rylov Yu. A. (2008) Granular geometry of
space-time as a result of Newtonian investigation strategy
- Rylov Yu. A. (2008) Why does the
Standard Model fail to explain the elementary particles structure?
Available at http://arXiv.org/abs/0810.0982
- Rylov Yu. A. (2008) Discriminating
properties of the space-time compactification Available at http://arXiv.org/abs/0809.2516
- Rylov Yu. A. (2008) Geometries
with intransitive equivalence relation Available at http://arXiv.org/abs/0807.2034
- Rylov Yu. A. (2008) Multivariance
as a crucial property of microcosm Available at http://arXiv.org/abs/0806.1716
- Rylov Yu. A. (2008) Geometrical
dynamics: spin as a result of rotation with superluminal speed Available at http://arXiv.org/abs/0801.1913
- Rylov Yu. A. (2007) Discrimination
of particle masses in multivariant space-time geometry Available at http://arXiv.org/abs/0712.1335
- Rylov Yu. A. (2007) Different
conceptions of Euclidean geometry Available at http://arXiv.org/abs/0709.02755
- Rylov Yu. A. (2007) Deformation
principle and further geometrization of physics Available at http://arXiv.org/abs/0704.3003
- Rylov Yu. A. (2007) Non-Euclidean
method of the generalized geometry construction and its application to
space-time geometry Available at http://arXiv.org/abs/Math.GM/0702552
- Rylov Yu. A. (2006) Non-Riemannian
geometry as a reason of the third modification of the space-time geometry Available at http://arXiv.org/abs/physics/0612138
- Rylov Yu. A. (2006) Crisis
in the geometry development and its social consequences Available at http://arXiv.org/abs/math.GM/0609765
- Rylov Yu. A. (2005) Euclidean
geometry as algorithm for construction of generalized geometries.
- Rylov Yu. A. (2005) " Tubular geometry
construction as a reason for new revision of the space-time conception." (Printed in What is Geometry?
polimetrica Publisher, Italy,
pp.201-235 http://www.polimetrica.com/polimetrica/406/
)
- Rylov Yu. A. (2005) " New crisis
in geometry?." (Available at http://arXiv.org/abs/mat.GM/0503261)
- Rylov Yu. A. (2004) "Deformation
principle as a foundations of physical geometry and its application to the
space-time geometry".Ãèïåðêîìïëåêñíûå ÷èñëà â ãåîìåòðèè è ôèçèêå 2,
69-96, (2004).(Available at http://arXiv.org/abs/physics/0411103)
- Rylov Yu. A. (2004) "Coordinateless
description and deformation principle as a foundations of physical
geometry”
. (Available at
http://arXiv.org/abs/math.GM/0031260)
- Rylov Yu. A. (2003) " Deformation
principle and problem of parallelism in geometry and physics." (Modification of
"Problem of parallelism in geometry and physics")
- RylovYu.A. (2002) "Associatie
delusions and problem of their overcoming".
- Rylov Yu. A. (2002) "Asymmetric
nondegenerate geometry". Proc.
of XXV workshop on the fundamental problems on high energy physics and
field theory. Protvino, June 25-28 (2002) pp 154-190. ((Available at
http://arXiv.org/abs/math.MG/0205061)
- Rylov Yu.A. (2002) "The Euclidean geometry deformations and capacities of
their application to microcosm space-time geometry".( Available
at http://arXiv.org/abs/physics/0206017)
- Rylov Yu.A. (2002) "Dynamics of stochastic systems and pecularities of
measurements in them". (Available at
http://arXiv.org/abs/physics/0210003).
- Rylov Yu.A. (2002) "Restricted linear properties of scalar product in
T-geometry".
- Rylov Yu.A. (2002) "Problem of parallelism in geometry and physics".
- Rylov Yu.A. (2000)
"Geometry without topology" (It
is slightly modified paper "Sigma-immanent form of Euclidean
geometry...") (Available at http://arXiv.org/abs/math.MG/0002161
).
- Rylov Yu.A. (1999) "Sigma-immanent form of the Euclidean geometry as a basis
for non-Euclidean geometry."
- Rylov
Yu.A. (1999) "Metric space: classification
of finite subspaces instead of constraints on metric." Proceedings
on analysis and geometry, Novosibirsk,
Publishing House of Mathematical institute, 2000. pp. 481-504, (in
Russian). English version: (Available at http://arXiv.org/abs/math.MG/9905111).
- Rylov Yu.A. (1999) "Description of
metric space as a classification of its finite subspaces." Fundamental'naya
i Prikladnaya Matematika, 7, no.4, 1147-1175, (2001). (in
Russian)
- Rylov Yu.A. (1999) "Introduction to
nondegenerate geometry." (monograph in Russian, about 170pp)Preface in English, Preface in
English
- , Short author’s
review in English, Detailed author’s review in English (Postscript format about 20 pp).
class=Section2>
- Rylov
Yu.A. (1995): "Space-time distortion as a reason for quantum
stochasticity" in Chaos: the interplay between stochastic and
deterministiic behaviour. Eds. P.Garbachewski, M.Wolf, A.Weron,
Karpacz'95 Proc.Lecture Notes in Physics. vol. 457, Springer, Berlin, pp.
523-529.
- Rylov
Yu.A. (1991): "Non-Riemannian
model of the space-time responsible for quantum effects". Journ.
Math. Phys. 32(8), 2092-2098, (1991).
- Rylov Yu.A. (1990) "Extremal properties of
Synge's world function and discrete geometry" . J.Math. Phys.
31, 2876-2890, (1990).
- Rylov Yu.A. (1970): "On connection between
the energy-momentum vector and canonical momentum in relativistic
mechanics". Teoretischeskaya i Matematischeskaya Fizika. 2,
333-337.(in Russian). Theor. and Math. Phys. (USA), 5, 333,
(1970) (trnslated from Russian)
- Rylov Yu.A. (1964): "Relative
gravitational field and conservation laws in general relativity". Ann.
Phys.(Leipzig) 12, 329-353.
- Rylov Yu.A. (1964): "Particles of
half-integer spin in universal 6-dimensional space". Vestnik
Moskovskogo Universiteta ser. fiz-astr. No 3, 13. (in Russian)
- Rylov Yu.A. (1963): "On universal
6-dimensional space". Vestnik Moskovskogo Universiteta ser.
fiz-astr. No 6, 23. (in Russian)
- Rylov Yu.A. (1963): "Normal
coordinates and the general relativity principle" Vestnik
Moskovskogo Universiteta ser. fiz.-astr. No 3, 55. (in Russian)
- Rylov Yu.A. (1962): "On relative
energy of static spherically symmetric gravitational field". VestnikMoskovskogo
Universiteta ser. fiz. No 6, 45. (in Russian)
- Rylov Yu.A. (1962): "On relative
localization of the gravitational field". Vestnik Moskovskogo
Universiteta No.5, 70. (in Russian)
- Rylov Yu.A. (1962): "On a possibility
of the Riemannian space description in terms of a finite interval".
Izvestiya Vysshikh Uchebnych Zavedenii, Matematika. No.3(28), 131-142.
(in Russian)
- Rylov Yu.A. (1961):"On singularity on
the gravitational radius at the Schwarzschild solution". Zhurnal
Eksperimental'noi i Teoretischeskoi Fiziki. 40, 1041. (in
Russian) .