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A General Differential Geometry with Two Types of Linear Connection


Wyman, Max (1940) A General Differential Geometry with Two Types of Linear Connection. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/92JW-1918.


The object of this thesis was the study of a differential geometry for a Hausdorff space endowed with an affine linear connection and a non-holonomic linear connection. The coordinate spaces were taken to be Banach spaces. In Chapter II we define the notion of a non-holonomic contravariant vector field, and by means of the non-holonomic linear connection introduce the operation of covariant differentiation. It was then found that many of the formal tensor theorems carried over to such spaces. For certain types of Hausdorff space it is possible to develop a normal representation theory, and by means of it to obtain normal non-holonomic vector forms. This then enables us to generalize the Michal-Hyers replacement theorem for differential invariants. Chapter IV is concerned with the determination of nonholonomic linear connections. This leads to the consideration of interspace adjoints for linear functions. In the main the results obtained in this thesis are generalizations of results obtained for finite dimensional spaces by A.D. Michal and J. L. Botsford. However the projective theory developed in Chapter V is new for spaces of finite dimension.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Michal, Aristotle D.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1940
Record Number:CaltechETD:etd-08262008-145426
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3234
Deposited By: Imported from ETD-db
Deposited On:26 Aug 2008
Last Modified:17 Aug 2023 00:31

Thesis Files

PDF (Wyman_m_1940.pdf) - Final Version
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