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Differential geometry is the study of Riemannian Manifolds. Differential geometry deals with metrical notions on Manifolds, while Differential Topology deals with those nonmetrical notions of Manifolds.
See also Differential Topology
References
Eisenhart, L. P. A Treatise on the Differential Geometry of Curves and Surfaces. New York: Dover, 1960.
Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, 1993.
Kreyszig, E. Differential Geometry. New York: Dover, 1991.
Lipschutz, M. M. Theory and Problems of Differential Geometry. New York: McGraw-Hill, 1969.
Spivak, M. A Comprehensive Introduction to Differential Geometry, 2nd ed, 5 vols.
Berkeley, CA: Publish or Perish Press, 1979.
Struik, D. J. Lectures on Classical Differential Geometry. New York: Dover, 1988.
Weatherburn, C. E. Differential Geometry of Three Dimensions, 2 vols. Cambridge, England: Cambridge University Press, 1961.
Differential Geometry