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Geometria Differenziale by Marco Abate, Francesca Tovena

Geometria Differenziale

by Marco Abate , Francesca Tovena
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Book cover type: Paperback
  • ISBN13: 9788847019195
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 472
  • Original Price: EUR 31.68
  • Language: Italian
  • Edition: 2011
  • Item Weight: 676 grams
  • BISAC Subject(s): Geometry / Differential

L'opera fornisce una introduzione alla geometria delle varietà differenziabili, illustrandone le principali proprietà e descrivendo le principali tecniche e i più importanti strumenti usati per il loro studio. Uno degli obiettivi primari dell'opera è di fungere da testo di riferimento per chi (matematici, fisici, ingegneri) usa la geometria differenziale come strumento; inoltre, grazie alla varietà degli aspetti della teoria in essa presentati, l'opera si presta ad essere utilizzata come libro di testo per corsi introduttivi alla geometria differenziale. Più in dettaglio, nell'opera saranno trattati i seguenti argomenti: richiami di algebra multilineare e tensoriale, spesso non presentati nei corsi standard di algebra lineare; varietà differenziali, incluso il teorema di Whitney; fibrati vettoriali, incluso il teorema di Frobenius; gruppi di Lie, incluso il teorema di corrispondenza fra sottogruppi e sottoalgebre; coomologia di de Rham, inclusa la dualità di Poincaré e il teorema di de Rham; connessioni, inclusa la teoria delle geodetiche; e geometria Riemanniana, con particolare attenzione agli operatori di curvatura e inclusi teoremi di Cartan- Hadamard, Bonnet-Myers, e Synge-Weinstein. Come abitudine degli autori, il testo è scritto in modo da favorire una lettura attiva, cruciale per un buon apprendimento di argomenti matematici; inoltre è corredato da diversi esempi svolti e numerosi esercizi proposti.

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