Theory and applications of abstract normal coordinates in a general differential geometry

Aristotle D. Michal; Donald H. Hyers

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1938)

  • Volume: 7, Issue: 2, page 157-175
  • ISSN: 0391-173X

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Michal, Aristotle D., and Hyers, Donald H.. "Theory and applications of abstract normal coordinates in a general differential geometry." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 7.2 (1938): 157-175. <http://eudml.org/doc/82952>.

@article{Michal1938,
author = {Michal, Aristotle D., Hyers, Donald H.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Functional analysis, function spaces},
language = {eng},
number = {2},
pages = {157-175},
publisher = {Scuola normale superiore},
title = {Theory and applications of abstract normal coordinates in a general differential geometry},
url = {http://eudml.org/doc/82952},
volume = {7},
year = {1938},
}

TY - JOUR
AU - Michal, Aristotle D.
AU - Hyers, Donald H.
TI - Theory and applications of abstract normal coordinates in a general differential geometry
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1938
PB - Scuola normale superiore
VL - 7
IS - 2
SP - 157
EP - 175
LA - eng
KW - Functional analysis, function spaces
UR - http://eudml.org/doc/82952
ER -

References

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  1. A.D. Michal and D.H. Hyers: (1). Second Order Differential Equations with Two Point Boundary Conditions in Ge-neral Analysis. American Journ. of Math., vol. 58 (1936), pp. 646-660. Zbl0014.31402JFM62.0457.01
  2. S. Banach: (1). Théorie des Opérations Lineaires (1932). Zbl0005.20901
  3. B. Riemann: (1). Commentatio Mathematica. Werke, 2nd ed., p. 391. 
  4. J.H.C. Whitehead: (1). On the Covering of a Complete Space by the Geodesics Through a Point. Annals of Math., vol. 36 (1935), pp. 679-704. Zbl0012.27802
  5. T.H. Hildebrandt and L.M. Graves: (1). Implicit Functions and Their Differentials in General Analysis. Trans. of Amer. Math. Soc., vol. 29 (1927), pp. 127-153. Zbl53.0234.02JFM53.0234.02
  6. M. Frechet: (1). La Differentielle dans l'Analyse Générale. Annales Sc. de l'Ecole Normale Superieure, vol. 42 (1925), pp. 293-323. Zbl51.0312.03JFM51.0312.03
  7. L.M. Graves: (1). Implicit Functions and Differential Equations in General Analysis. Trans. of Amer. Math. Soc., vol 29 (1927), pp. 514-552. Zbl53.0234.04JFM53.0234.04
  8. A.D. Michal and R.S. Martin: (1). Some Expansions in Vector Space. Journal de Mathématiques Pures et Appliquées, vol. 13 (1934), pp. 69-91. Zbl0009.02301JFM60.0327.02
  9. M. Kerner: (1). Sur les Variations Faibles et Fortes d'une Fonctionnelle. Annali di Matematica, vol. 10 (1931-1932), pp. 145-164. Zbl0003.40202JFM58.0426.01
  10. (2). La Differentielle dans l'Analyse Générale. Annals of Mathematics, vol. 34 (1933), pp. 546-572. 
  11. A.D. Michal: (1). Postulates for a Linear Connection. Annali di Matematica, vol. 15 (1936), pp. 197-220. Zbl0016.21502JFM62.1477.03
  12. (2). Riemannian Differential Geometry in Abstract Spaces. Proc. of the Nat. Acad. of Sc., vol. 21 (1935), pp. 526-529. Zbl0012.31603
  13. (3). General Tensor Analysis. Bull. of Amer. Math. Soc., vol. 43 (1937), pp. 394-401. 
  14. (4). Abstract Covariant Vector Fields in a General Absolute Calculus. Amer. Journal of Math., vol. 59 (1937), pp. 306-314. Zbl0017.02201
  15. (5). General Riemannian Differential Geometry, to be published elsewhere. 
  16. (6). Affinely Connected Function Space Manifolds. American Journ. of Math., vol. 50 (1928), pp. 473-517. Zbl54.0428.01
  17. (7). Differential Geometries of Function Space. Proc. of Nat. Acad. of Sc., vol. 16 (Jan., 1930), pp. 88-94. Zbl56.1192.02
  18. (8). The Differential Geometry of a Continuous Infinitude of Contravariant Functional Vectors. Proc. of Nat. Acad. of Sc., vol. 16 (1930), pp. 162-164. Zbl56.1192.03
  19. (9). Projective Functional Tensors and Other Allied Functionals. Proc. of Nat. Acad. of Sc., vol. 16 (1930), pp. 165-168. Zbl56.1193.01
  20. (10). Function Space-Time Manifolds. Proc. of Nat. Acad. of Sc., vol. 17 (1931), pp. 217-225. Zbl0001.34203
  21. A. Kawaguchi: (1). Die Differentialgeometrie in den Verschiedenen Funktionalräumen. I. Vektorialen und Tensorialen. Journal of Hokkaido Imperial University, vol. III (1935), pp. 43-106. Zbl0013.11903JFM61.1449.01
  22. F. Hausdorff: (1). Mengenlehre (1927). Zbl53.0169.01
  23. A.D. Michal and E.W. Paxson: (1). Maps of Abstract Topological Spaces in Banach Spaces. Bull. of Amer. Math. Soc., vol. 42 (1936), pp. 529-534 and a forthcoming addendum. Zbl0015.00605JFM62.0460.02
  24. O. Veblen and J.H.C. Whitehead: (1). The Foundations of Differential Geometry. Cambridge Tract n.° 29 (1932). Zbl0005.21801JFM58.0754.01
  25. A.D. Michal and V. Elconin: (1). Differential Properties of Abstract Transformation Groups with Abstract Parameters. American Journ. of Math., vol. 59 (Jan., 1937), pp. 129-143. Zbl0015.39401JFM63.1001.02
  26. (2). Completely Integrable Differential Equations in Abstract Spaces. Acta Mathematica, vol. 68 (1937), pp. 71-107, Zbl63.0360.01
  27. R.S. Martin: (1). Contributions to the Theory of Functionals. (California Institute of Technology thesis (unpublished)). June, (1932). 
  28. O. Veblen: (1). Invariants of Quadratic Differential Forms. (Cambridge tract (1927)). Zbl53.0681.01JFM53.0681.01
  29. (2). Normal Coordinates for the Geometry of Paths. Proc. of Nat. Acad. of Se., vol. 8 (1922), pp. 192-197. 
  30. A.D. Michal and T.Y. Thomas: (1). Differential Invariants of Relative Quadratic Differential Forms. Annals of Math., vol. 28 (1927), pp. 631-688. Zbl53.0684.03JFM53.0684.03
  31. (2). Differential Invariants of Affinely Connected Manifolds. Annals of Math., vol. 28 (1927), pp. 196-236. Zbl53.0684.02
  32. L.P. Eisenhart: (1). Non-Riemannian Geometry. Colloquium publications of A. M. S. (1927). JFM52.0721.02
  33. T.Y. Thomas: (1). Differential Invariants of Generalized Spaces (1934). Zbl0009.08503
  34. (2). On Normal Coordinates. Proc. of Nat. Acad. of Sc., vol. 22 (1936), pp. 309-312. Zbl0014.18001
  35. O. Veblen and T.Y. Thomas: (1). The Geometry of Paths, Transactions of A. M. S., vol. 25 (1923), pp. 551-608. Zbl50.0504.02JFM50.0504.02
  36. F. Conforto: (1). Sopra il calcolo differenziale assoluto negli spazi funzionali continui. Annali di Pisa, vol. 2 (1933), pp. 309-324. Zbl59.1345.03JFM59.1345.03

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