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Local geometry of Carnot manifolds under minimal smoothness
Local geometry of Carnot manifolds under minimal smoothness,10.1134/S1064562407020172,Doklady Mathematics,S. K. Vodop’yanov,M. B. Karmanova
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Local geometry of Carnot manifolds under minimal smoothness
(
Citations: 17
)
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S. K. Vodop’yanov
,
M. B. Karmanova
Journal:
Doklady Mathematics  DOKL MATH
, vol. 75, no. 2, pp. 240246, 2007
DOI:
10.1134/S1064562407020172
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Citation Context
(8)
...Recall some basic notions and facts of the theory of Carnot–Carath´ eodory spaces following the approach of [9,
30
, 31]...
...Proposition 14 (local approximation theorem [9, 14,
30
], compare with [7, 8])...
S. V. Selivanova
.
The tangent cone to a quasimetric space with dilations
...It is well known
9
,
15
,
16
that vector fields where
Maria Karmanova
,
et al.
An area formula for contact C mappings of Carnot manifolds
...Following [6,
7
], we equip some neighborhood of an arbitrary point g ∈ M with the structure of a Carnot group...
A. D. Kozhevnikov
.
Inverse and implicit function theorems on carnot manifolds
...Mitchell [16], Bella¨õche [2], the paper of Gromov asking for an intrinsic point of view for subriemannian geometry [12], Margulis, Mostow [14], [15], dedicated to Rademacher theorem for subriemannian manifolds and to the construction of a tangent bundle of such manifolds, and Vodopyanov [20] [21], Vodopyanov and K
ar
manova [22], fundamental results concerning the intrinsic properties of subriemannian spaces endowed with the ...
... results by Bella¨õche [2], first to speak about normal frames, providing rigorous proofs for this existence in a flow of results between theorem 4.15 and ending in the first half of section 7.3 (page 62), Gromov [12] in his approximation theorem p. 135 (conclusion of the point (a) below), as well in his convergence results concerning the nilpotentization of vector fields (related to point (b) below), Vodopyanov and others [
20
] ...
Marius Buliga
.
A characterization of subriemannian spaces as length dilatation struc...
...Main results of Section 2 are formulated in short communications [
132
, 133]...
Maria Karmanova
,
et al.
Geometry of CarnotCarath\'{e}odory Spaces, Differentiability and Coa...
References
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(
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G. A. Margulis
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G. D. Mostow
Journal:
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, vol. 80, no. 1, pp. 299317, 2000
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Citations
(17)
The tangent cone to a quasimetric space with dilations
(
Citations: 4
)
S. V. Selivanova
Journal:
Siberian Mathematical Journal  SIB MATH JENGL TR
, vol. 51, no. 2, pp. 313324, 2010
An area formula for contact C mappings of Carnot manifolds
(
Citations: 4
)
Maria Karmanova
,
Sergey Vodopyanov
Journal:
Complex Variables and Elliptic Equations
, vol. 55, no. 13, pp. 317329, 2010
Inverse and implicit function theorems on carnot manifolds
A. D. Kozhevnikov
Journal:
Siberian Mathematical Journal  SIB MATH JENGL TR
, vol. 51, no. 6, pp. 10471060, 2010
Algebraic and analytic properties of quasimetric spaces with dilations
Svetlana Selivanova
,
Sergey Vodopyanov
Published in 2010.
Tangent cone to a regular quasimetric CarnotCarathéodory space
(
Citations: 5
)
S. V. Selivanova
Journal:
Doklady Mathematics  DOKL MATH
, vol. 79, no. 2, pp. 265269, 2009