9c6c8fc5bd-p-06.pdf

# 9c6c8fc5bd-p-06.pdf - INDICE GENERAL ix derivaciones A...

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´ INDICE GENERAL ix / derivaciones. A pesar de las redundancias y poca econom´ ıa l´ogica que esto supone, creemos que as´ ı se hacen m´as asimilables esos conceptos. Parte II. Temas 5–7. Se estudian objetos geom´ etricos elementales sobre una variedad diferenciable, hasta un primer contacto con la geometr´ ıa riemanniana. Aparte del tratamiento algebraico de campos tensoriales sobre la variedad, se introducen: (i) campos vectoriales (curvas inte- grales, flujos), (ii) formas diferenciales (circulaci´on, formas cerradas y exactas) y (iii) m´ etricas riemannianas o, con m´as generalidad, semi- riemannianas. Ponemos especial inter´ es en mostrar c´omo, fijada una tal m´ etrica, los conceptos asociados a formas diferenciales pueden apli- carse a campos vectoriales (y viceversa). La utilidad de las m´ etricas riemannianas, y su f´acil asimilaci´on intuitiva, hacen que anticipemos algunos conceptos, como el de distancia asociada, que se estudian con m´as detalle posteriormente. As´ ı, al terminar esta segunda parte, el lec- tor habr´a adquirido unas nociones m´
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