Manifold Riemann

Dalam geometri diferensial, sebuah manifold Riemann atau ruang Riemannan $(M,g)$ adalah sebuah manifold mulus real $M$ yang dilengkapi dengan sebuah darab dalam $g_{p}$ di ruang garis singgung $T_{p}M$ di setiap titik $p$ . Jika $X$ dan $Y$ adalah medan vektor pada $V$ , maka $p\mapsto g_{p}(X(p),Y(p))$ merupakan sebuah fungsi mulus. Keluarga $g_{p}$ dari darab dalam disebut sebuah metrik Riemann (tensor). Istilah ini diambil dari nama matematikawan Jerman Bernhard Riemann. Studi mengenai manifold Riemann ini melingkupi subjek yang disebut geometri Riemann.

Metrik Riemann (tensor) membuatnya memungkinkan untuk mendefinisikan berbagai titik geometrik pada sebuah manifold Riemann, seperti sudut, jarak kurva, luas (atau volume), kelengkungan, gradien fungsi dan kedivergenan medan vektor.

Referensi

Jost, Jürgen (2008), Riemannian Geometry and Geometric Analysis (edisi ke-5th), Berlin, New York: Springer-Verlag, ISBN 978-3-540-77340-5
do Carmo, Manfredo (1992), Riemannian geometry, Basel, Boston, Berlin: Birkhäuser, ISBN 978-0-8176-3490-2 [1]

Pranala luar

L.A. Sidorov (2001) [1994], "Riemannian metric", dalam Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4

Pengawasan otoritas
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Perpustakaan nasional	Spanyol Prancis (data) Amerika Serikat Jepang Republik Ceko
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