Base natural

Base natural

Base natural

En geometría diferencial, una base natural es un tipo base vectorial del espacio tangente a una variedad diferenciable que puede ser asociada naturalmente a un sistema de coordenadas curvilíneo.

Definición de base natural

Dada una variedad diferenciable \mathcal{M} de dimensión n y un conjunto de n campos vectoriales V_1,...,V_n\;\in T\mathcal{M} definidos sobre un conjunto abierto A esa variedad tales que en cada punto forman una base vectorial del espacio tangente a la variedad, es una base natural si y sólo si existe una carta local o sistema de coordenadas local \varphi:A \subset \mathcal{M} \to \R^n \land \varphi(P) \mapsto (x_1(P),...,x_n(P)) que cumpla alguna de las siguientes condiciones:

  1. Los campos vectoriales coinciden con las derivadas a lo largo de las curvas coordenadas asociadas a las coordenadas locales: {V_i|}_P = \left(\part_{x_i}\right)_P.
  2. La base dual asociada a los n campos vectoriales en cada punto, está formada por 1-formas exactas, es decir, existen \theta^1,...,\theta^n\ \in T^*\mathcal{M} y una carta local, como la descrita anteriormente, tal que \theta^i(V_j) =\delta_j^i y \theta^i = dx^i\;.
Obtenido de "Base natural"

Wikimedia foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Mira otros diccionarios:

  • Base 32 — This article is about the positional numerical system. For the content encoding scheme, see Base32. Numeral systems by culture Hindu Arabic numerals Western Arabic (Hindu numerals) Eastern Arabic Indian family Tamil Burmese Khmer Lao Mongolian… …   Wikipedia

  • Natural logarithm — Base e redirects here. For the numbering system which uses e as its base, see Non integer representation#Base e. Graph of the natural logarithm function. The function slowly grows to positive infinity as x increases and rapidly goes to negative… …   Wikipedia

  • Natural gas storage — Natural gas, like many other commodities, can be stored for an indefinite period of time in natural gas storage facilities for later consumption. Contents 1 Usage 2 Measures and definitions 3 Types 3.1 …   Wikipedia

  • Natural Selection 2 — Éditeur Unknown Worlds Entertainment Développeur Unknown Worlds Entertainment Concepteur Charlie Cleveland Date de sortie Début 2010 Genre jeu de tir subjectif …   Wikipédia en Français

  • Natural Selection (videojuego) — Natural Selection Desarrolladora(s) Unknown Worlds Entertainment Diseñador(es) Charlie Cleveland Motor GoldSrc Plataforma(s) …   Wikipedia Español

  • Natural language user interface — Natural Language User Interfaces (LUI) are a type of computer human interface where linguistic phenomena such as verbs, phrases and clauses act as UI controls for creating, selecting and modifying data in software applications. In interface… …   Wikipedia

  • Natural Resources Research Institute — Natural Resources Research Institute. The Natural Resources Research Institute (NRRI) is a U.S. based research institute established by the Minnesota state legislature within the University of Minnesota Duluth. NRRI is a non profit applied… …   Wikipedia

  • Natural — Nat u*ral (?; 135), a. [OE. naturel, F. naturel, fr. L. naturalis, fr. natura. See {Nature}.] 1. Fixed or determined by nature; pertaining to the constitution of a thing; belonging to native character; according to nature; essential;… …   The Collaborative International Dictionary of English

  • Natural day — Natural Nat u*ral (?; 135), a. [OE. naturel, F. naturel, fr. L. naturalis, fr. natura. See {Nature}.] 1. Fixed or determined by nature; pertaining to the constitution of a thing; belonging to native character; according to nature; essential;… …   The Collaborative International Dictionary of English

  • Natural fats — Natural Nat u*ral (?; 135), a. [OE. naturel, F. naturel, fr. L. naturalis, fr. natura. See {Nature}.] 1. Fixed or determined by nature; pertaining to the constitution of a thing; belonging to native character; according to nature; essential;… …   The Collaborative International Dictionary of English

Compartir el artículo y extractos

Link directo
… Do a right-click on the link above
and select “Copy Link”