The geometric notion meaning that at some point two curves (or a curve and a surface) hav
See also [[Tangent vector|Tangent vector]].
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$#C+1 = 32 : ~/encyclopedia/old_files/data/V096/V.0906340 Vector,
''geometric''
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that associates with a differentiable vector field $ X $
and a differentiable geometric object $ Q $
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''of an operator (transformation) $A$ of a vector space $L$ over a field $k$''
An element $\lambda\in k$ such that there is a non-zero vector $x\in L$ satisfying the condition
2 KB (373 words) - 09:18, 12 December 2013
...is called Euclidean if each of its fibres has the structure of a Euclidean vector space with a scalar product $ \langle , \rangle $
is a smooth function on the base. A linear connection on a Euclidean vector bundle is called a Euclidean connection if for any parallel displacement of
2 KB (251 words) - 19:38, 5 June 2020
$#C+1 = 17 : ~/encyclopedia/old_files/data/D030/D.0300210 Darboux vector
The vector $ \pmb\delta $
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...ocity vector|Phase velocity vector]]) is defined, is non-zero and is not a vector tangent to the curve. The concept was introduced by H. Poincaré [[#Referen
...="top">[2]</TD> <TD valign="top"> S. Lefshetz, "Differential equations: geometric theory" , Interscience (1962)</TD></TR></table>
2 KB (281 words) - 18:48, 5 April 2020
...concentration of its probability distribution around a certain prescribed vector in terms of the second-order moments. Let $ X $
be a random vector assuming values $ x = ( x _ {1}, \dots, x _ {n} ) ^ {T} $
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Let a geometric object $ \Omega $(
cf. [[Geometric objects, theory of|Geometric objects, theory of]]) be given in a differentiable manifold $ X _ {n} $,
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...f $K$ along any non-zero integer vector. Here the "width" of $K$ along a vector $v$ in $\mathbf{R}^n$ is
The width of $K$ with respect to $\mathbf{Z}^n$ is greater or equal than the geometric width of $K$, which is the minimum width of $K$ along all unit-length vecto
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Adjoint norms (cf. [[Norm|Norm]]) in certain vector spaces dual to each other.
vector $ \alpha $,
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...cyclopediaofmath.org/legacyimages/c/c025/c025470/c02547012.png" /> for any
vector field <img align="absmiddle" border="0" src="https://www.encyclopediaofmath
...02547060.png" /> (and this is equivalent). It is sometimes called the Reeb
vector field of <img align="absmiddle" border="0" src="https://www.encyclopediaofm
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...beginning of the 20th century. It differs from local geometry, in which a geometric object (field, mapping) is studied in sufficiently small domains only, as i
...ative results, as well as quantitative relations in the large, for regular geometric structures on multi-dimensional singularity-free manifolds.
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is a differential-geometric structure on $ M $
...ant differentiation|covariant differentiation]], which associates with two vector fields $ X , Y $
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...nifold similar to a [[Sasakian manifold]]. However, by its topological and geometric properties, such a manifold is closely related to a product manifold (unlik
...$(M,g)$ endowed with an endomorphism $\phi$ of the tangent bundle $TM$, a vector field $\xi$ and a $1$-form $\eta$ which satisfy the conditions
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...lidean space]] of signature $(1,3)$, suggested by H. Minkowski (1908) as a geometric model of space-time in the special theory of relativity (see ). Correspondi
...e is a time-like vector. The tangent vector to a light ray is an isotropic vector.
5 KB (692 words) - 19:18, 12 April 2014
A geometric object described in a coordinate system $ x = ( x ^ {1}, \dots, x ^ {n}
the tensor density is a tensor (cf. [[Tensor on a vector space|Tensor on a vector space]]). Concepts such as type, valency, covariance, contravariance, etc.
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...ping|Transversal mapping]]); a concept in linear algebra, differential and geometric topology.
a) Two vector subspaces $ A, B $
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...stable vector bundles (of fixed rank and degree; cf. also [[Vector bundle|Vector bundle]]) over a given [[Riemann surface|Riemann surface]] $X$ of genus $g\
...#References|[a5]]]; and quantized Hitchin systems with applications to the geometric Langlands program [[#References|[a2]]].
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''of a set $M$ in an $n$-dimensional vector space''
In general vector spaces, where a hyperplane can be defined as a domain of constant value of
2 KB (331 words) - 04:59, 16 September 2014