Global analysis describes diverse yet interrelated research areas in analysis and algebraic geometry, particularly those in which Kunihiko Kodaira made his most outstanding contributions to mathematics. The eminent contributors to this volume, from Japan, the United States, and Europe, have prepared original research papers that illustrate the progress and direction of current research in complex variables and algebraic and differential geometry. The authors investigate, among other topics, complex manifolds, vector bundles, curved 4-dimensional space, and holomorphic mappings. Bibliographies facilitate further reading in the development of the various studies.Originally published in 1970.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Global Analysis: Papers in Honor of K. Kodaira (Pms-29)

We consider locally symmetric almost Kenmotsu manifolds showing that such a manifold is a Kenmotsu manifold if and only if the Lie derivative of the structure, with respect to the Reeb vector field $\xi$, vanishes. Furthermore, assuming that for a $(2n+1)$-dimensional locally symmetric almost Kenmotsu manifold such Lie derivative does not vanish and the curvature satisfies $R_{XY}\xi =0$ for any $X, Y$ orthogonal to $\xi$, we prove that the manifold is locally isometric to the Riemannian product of an $(n+1)$-dimensional manifold of constant curvature $-4$ and a flat $n$-dimensional manifold. We give an example of such a manifold.

/pdf/almost-kenmotsu-manifolds-and-local-symmetry-197fv3ah40.pdf

Almost Kenmotsu manifolds and local symmetry

The monograph deals with the theory of conformal, geodesic,
holomorphically projective, F-planar and others mappings and
transformations of manifolds with affine connection,
Riemannian, Kahler and Riemann-Finsler manifolds. Concretely,
the monograph treats the following: basic concepts of
topological spaces, the theory of manifolds with affine
connection (particularly, the problem of semigeodesic
coordinates), Riemannian and Kahler manifolds (reconstruction
of a metric, equidistant spaces, variational problems in
Riemannian spaces, SO(3)-structure as a model of statistical
manifolds, decomposition of tensors), the theory of
differentiable mappings and transformations of manifolds (the
problem of metrization of affine connection, harmonic
diffeomorphisms), conformal mappings and transformations
(especially conformal mappings onto Einstein spaces, conformal
transformations of Riemannian manifolds), geodesic mappings
(GM; especially geodesic equivalence of a manifold with affine
connection to an equiaffine manifold), GM onto Riemannian
manifolds, GM between Riemannian manifolds (GM of equidistant
spaces, GM of Vn(B) spaces, its field of symmetric linear
endomorphisms), GM of special spaces, particularly Einstein,
Kahler, pseudosymmetric manifolds and their generalizations,
global geodesic mappings and deformations, GM between
Riemannian manifolds of different dimensions, global GM,
geodesic deformations of hypersurfaces in Riemannian spaces,
some applications of GM to general relativity, namely three
invariant classes of the Einstein equations and geodesic
mappings, F-planar mappings of spaces with affine connection,
holomorphically projective mappings (HPM) of Kahler manifolds
(fundamental equations of HPM, HPM of special Kahler manifolds,
HPM of parabolic Kahler manifolds, almost geodesic mappings,
which generalize geodesic mappings, Riemann-Finsler spaces and
their geodesic mappings, geodesic mappings of Berwald spaces
onto Riemannian spaces.

Differential Geometry of Special Mappings

* Basic Algebraic Notions* Basic Geometrical Notions* Walker Structures* Three-Dimensional Lorentzian Walker Manifolds* Four-Dimensional Walker Manifolds* The Spectral Geometry of the Curvature Tensor* Hermitian Geometry* Special Walker Manifolds

The Geometry of Walker Manifolds

We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.

A survey on cosymplectic geometry

We show that a non-Sasakian contact metric manifold whose characteristic vector field belongs to the $(k,\mu)$-nullity distribution is completely determined locally by its dimension and the values for $k$ and $\mu$. We present explicit examples for all possible dimensions and all possible $(k,\mu)$.

/pdf/a-full-classification-of-contact-metric-k-mu-spaces-21ti4iva8x.pdf

A full classification of contact metric $(k,\mu)$-spaces

Definition and early development local structure of semi-symmetric spaces explicit treatment of foliated semi-symmetric spaces curvature homogeneous semi-symmetric spaces asymptotic distributions and algebraic rank three-dimensional Riemannian manifolds of conullity two asymptotically foliated semi-symmetric spaces elliptic semi-symmetric spaces complete foliated semi-symmetric spaces application - local rigidity problems for hypersurfaces with type number two in IR4 three-dimensional Riemannian manifolds of relative conullity two appendix - more about curvature homogeneous spaces.

Riemannian Manifolds of Conullity Two

Characteristic reflections on unit tangent sphere bundles

We show that the geodesic flow vector field on the unit tangent sphere bundle of a two-point homogeneous space is both minimal and harmonic and determines a harmonic map. For a complex space form, we exhibit additional unit vector fields on the unit tangent sphere bundle with those properties. We find the same results for the corresponding unit vector fields on the pointed tangent bundle. Moreover, the unit normal to the sphere bundles in the pointed tangent bundle of any Riemannian manifold always enjoys those properties.

Harmonic and minimal vector fields on tangent and unit tangent bundles

As a first step in the search for curvature homogeneous unit tangent sphere bundles we derive necessary and sufficient conditions for a manifold to have a unit tangent sphere bundle with constant scalar curvature. We give complete classifications for low dimensions and for conformally flat manifolds. Further, we determine when the unit tangent sphere bundle is Einstein or Ricci-parallel.

/pdf/unit-tangent-sphere-bundles-with-constant-scalar-curvature-5o2eb15rw0.pdf

Eric Boeckx

Papers

A full classification of contact metric $(k,\mu)$-spaces

Riemannian Manifolds of Conullity Two

Characteristic reflections on unit tangent sphere bundles

Harmonic and minimal vector fields on tangent and unit tangent bundles

Unit Tangent Sphere Bundles with Constant Scalar Curvature