Let f : S → S(^4) be an immersion of a Riemann surface in the 4-sphere. The thesis begins with a study of the adapted moving frame of / in order to produce conditions for certain naturally defined lifts to SO(5)/U(2) and S0(5)T(^2) to be conformal, harmonic and holomorphic with respect to two different but naturally occuring almost complex structures. This approach brings together the results of a number of authors regarding lifts of conformal, minimal immersions including the link with solutions of the Toda equations. Moreover it is shown that parallel mean curvature immersions have haj-monic lifts into S0(5)/U(2).A certain natural lift of / into CP(^3), the twistor space of S(^4), is studied more carefully via an explicit description and in the case of / being a conformal immersion this gives a beautiful and simple formula for the lift in terms of a stereographic co-ordinate associated to /. This involves establishing explicitly the two-to-one correspondence between elements of the matrix groups Sp(2) and SO(5) and working with quaternions. The formula enables properties of such lifts to be explored and in particular it is shown that the harmonic sequence of a harmonic lift is either finite or satisfies a certain symmetry property. Uniqueness properties of harmonic lifts are also proved. Finally, the ideas are extended to the hyperbolic space H(^4) and after an exposition of the twistor fibration for this case, a method for constructing superminimal immersions of surfaces into H'^ from those in S"' is given.

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Thesis (M.S.)--University of Wisconsin--Madison, 1974. / Title from title screen (viewed May 13, 2009). Includes bibliographical references. Online version of print original.

Univ., Diss.--Sendai.

Inaug.-diss.--München. / Lebenslauf. Multigraphed. "Verzeichnis der benutzten literatur und karten": p. 101-106.

Thesis (Ph. D.)--University of California, Los Angeles, 1990. / Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of North Texas, Dec., 2009. / Title from title page display. Includes bibliographical references.

Thesis (doctoral)--Göteborgs universitet, 1987. / Added t.p. with thesis statement and abstract inserted. Includes bibliographical references (p. 142-150).

Thesis (M. Phil.)--University of Hong Kong, 1997. / Includes bibliographical references (leaf 61-66).

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 112-114). Also available via the Internet.