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1

Chern, Shiing-Shen. Riemann-Finsler geometry. World Scientific, 2005.

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2

1963-, Shen Zhongmin, ed. Riemann-Finsler geometry. World Scientific, 2005.

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3

Gardiner, Frederick P., Gabino Gonzalez-Diez, and Christos Kourouniotis, eds. Geometry of Riemann Surfaces. Cambridge University Press, 2009. http://dx.doi.org/10.1017/cbo9781139194266.

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4

Dragomir, Sorin, Mohammad Hasan Shahid, and Falleh R. Al-Solamy, eds. Geometry of Cauchy-Riemann Submanifolds. Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-0916-7.

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5

Barletta, E. Foliations in Cauchy-Riemann geometry. American Mathematical Society, 2007.

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6

Berliocchi, Henri. Infirmation de l'hypothèse de Riemann. Economica, 2001.

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7

Bao, D., S. S. Chern, and Z. Shen. An Introduction to Riemann-Finsler Geometry. Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1268-3.

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8

Dai-Wai, Bao David, ed. A sampler of Riemann-Finsler geometry. Cambridge University Press, 2004.

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9

Bao, David Dai-Wai. A sampler of Riemann-Finsler geometry. Cambridge University Press, 2010.

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10

Muñoz, José Luis. Riemann: Una visión nueva de la geometría. Nivola, 2006.

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11

service), SpringerLink (Online, ed. Teorema di Riemann-Roch e questioni connesse. Springer-Verlag Berlin Heidelberg, 2011.

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12

Buser, Peter. Geometry and spectra of compact Riemann surfaces. Birkhäuser, 1992.

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13

Hermann, Weyl. Riemanns geometrische Ideen, ihre Auswirkung und ihre Verknüpfung mit der Gruppentheorie. Springer, 1988.

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14

Pfahler, Eisenhart Luther. Riemannian geometry. Princeton University Press, 1997.

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15

Buser, Peter. Geometry and Spectra of Compact Riemann Surfaces. Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4992-0.

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16

Ji, Lizhen, Athanase Papadopoulos, and Sumio Yamada, eds. From Riemann to Differential Geometry and Relativity. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-60039-0.

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17

Seppälä, Mika. Geometry of Riemann surfaces and Teichmüller spaces. North-Holland, 1992.

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18

Faltings, Gerd. Lectures on the arithmetic Riemann-Roch theorem. Princeton University Press, 1992.

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19

Muñoz Porras, José M., Sorin Popescu, and Rubí E. Rodríguez, eds. The Geometry of Riemann Surfaces and Abelian Varieties. American Mathematical Society, 2006. http://dx.doi.org/10.1090/conm/397.

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20

Pfeffer, Washek F. The Riemann approach to integration: Local geometric theory. Cambridge University Press, 1993.

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21

Peter, Pesic, ed. Beyond geometry: Classic papers from Riemann to Einstein. Dover Publications, 2007.

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22

Scrimieri, Giorgio. Fondazione della geometria: Da Bernhard Riemann a Hermann Weyl = Über die Hypothesen, welche der Geometrie zu Grunde liegen. Congedo, 1992.

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23

1940-, Alekseevskiĭ Dmitriĭ Vladimirovich, and Baum Helga 1954-, eds. Recent developments in pseudo-Riemannian geometry. European Mathematical Society, 2008.

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24

Taniguchi, Tetsuya. Non-isotropic harmonic tori in complex projective spaces and configurations of points on Riemann surfaces. Tohoku University, 1999.

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25

D'Angelo, John P. Hermitian analysis: From Fourier series to Cauchy-Riemann geometry. Birkhauser/Springer, 2013.

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26

Boothby, William M. An introduction to differentiable manifolds and Riemannian geometry. 2nd ed. Academic Press, 2003.

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27

Aitken, Wayne. An arithmetic Riemann-Roch theorem for singular arithmetic surfaces. American Mathematical Society, 1996.

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28

H, Hubbard John, ed. Teichmuller theory and applications to geometry, topology, and dynamics. Matrix Editions, 2005.

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29

service), SpringerLink (Online, ed. Lectures on algebraic geometry. Vieweg, 2008.

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30

Nolte, David D. Geometry on my Mind. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805847.003.0005.

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This chapter reviews the history of modern geometry with a focus on the topics that provided the foundation for the new visualization of physics. It begins with Carl Gauss and Bernhard Riemann, who redefined geometry and identified the importance of curvature for physics. Vector spaces, developed by Hermann Grassmann, Giuseppe Peano and David Hilbert, are examples of the kinds of abstract new spaces that are so important for modern physics, such as Hilbert space for quantum mechanics. Fractal geometry developed by Felix Hausdorff later provided the geometric language needed to solve problems i
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31

Riemann-Finsler Geometry. World Scientific Publishing Co Pte Ltd, 2005.

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32

Geometry of Riemann Surfaces. Cambridge University Press, 2010.

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33

Gardiner, Frederick P., Gabino González-Diez, and Christos Kourouniotis. Geometry of Riemann Surfaces. Cambridge University Press, 2010.

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34

Gardiner, Frederick P., Gabino González-Diez, and Christos Kourouniotis. Geometry of Riemann Surfaces. Cambridge University Press, 2013.

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35

Gardiner, Frederick P., Gabino González-Diez, and Christos Kourouniotis. Geometry of Riemann Surfaces. Cambridge University Press, 2013.

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36

Willmore, T. J. Riemannian Geometry. Oxford University Press, 1997.

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37

Willmore, T. J. Riemannian Geometry. Oxford University Press, USA, 1997.

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38

Lang, Serge, and William Fulton. Riemann-Roch Algebra. Springer New York, 2010.

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39

Lang, Serge, and William Fulton. Riemann-Roch Algebra. Springer London, Limited, 2013.

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40

Dragomir, Sorin, Mohammad Hasan Shahid, Falleh R. Al-Solamy, and Shahid Mohammad Hasan. Geometry of Cauchy-Riemann Submanifolds. Springer, 2016.

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41

Bao, D., S. S. Chern, and Z. Shen. Introduction to Riemann-Finsler Geometry. Springer New York, 2012.

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42

Dragomir, Sorin, Mohammad Hasan Shahid, and Falleh R. Al-Solamy. Geometry of Cauchy-Riemann Submanifolds. Springer London, Limited, 2016.

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43

Dragomir, Sorin, Mohammad Hasan Shahid, and Falleh R. Al-Solamy. Geometry of Cauchy-Riemann Submanifolds. Springer, 2018.

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44

Bao, D., S. S. Chern, and Z. Shen. Introduction to Riemann-Finsler Geometry. Springer London, Limited, 2012.

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45

Riemanns geometrische Ideen, ihre Auswirkung und ihre Verknüpfung mit der Gruppentheorie. Springer Berlin Heidelberg, 1988.

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46

Kalinowski, Marek W. Riemann Waves and Their Applications. Wiley & Sons, Incorporated, John, 1993.

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47

Eisenhart, Luther Pfahler. Riemannian Geometry. Princeton University Press, 2016.

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48

Maurin, Krzysztof. Riemann Legacy: Riemannian Ideas in Mathematics and Physics. Springer, 2013.

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49

Ji, Lizhen, Athanase Papadopoulos, and Sumio Yamada. From Riemann to Differential Geometry and Relativity. Springer, 2017.

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50

Sorvali, T., and M. Seppälä. Geometry of Riemann Surfaces and Teichmüller Spaces. Elsevier Science & Technology Books, 2011.

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