TABLE OF CONTENTS -- Preface -- Personal and Professional History -- Sopra il Contatto di Due Curve Piane -- A Theorem on the Tangram -- 1. Introduction -- 2. Lemmas -- 3. Proof of the theorem -- 4. Remark -- Projective Differential Geometry of a Pair of Plane Curves -- 1. Introduction -- 2. Two projective invariants -- 3. The canonical triangle and geometrical characterizations of the invariants -- 4. Canonical power series expansions -- 5. A generalization of the covariant line of Bompiani -- An Invariant of Intersection of Two Surfaces -- 1. Introduction -- 2. Derivation -- 3. A projectively geometric characterization -- 4. A metrically geometric characterization -- Projective Invariants of a Pair of Surfaces -- 1. Introduction -- 2. A projective invariant -- 3. A geometrical characterization of the invariant I -- 4. Certain projective transformations and invariants -- Projective Invariants of Intersection of Certain Pairs of Surfaces -- 1. Introduction -- I. TWO SURFACES WITH DISTINCT TANGENT PLANES AND DISTINCT ASYMPTOTIC TANGENTS AT AN ORDINARY POINT -- 2. Derivation of invariants. -- 3. Projective characterizations of the invariants I J -- II . TWO SURFACES WITH DISTINCT TANGENT PLANES AND A COMMON ASYMPTOTIC TANGENT AT AN ORDINARY POINT -- 4. Derivation of an invariant. -- 5. A projective characterization of the invariant I -- REFERENCES -- Some Invariants of Certain Pairs of Hypersurfaces -- Introduction -- CHAPTER I. TWO HYPERSURFACES WITH COMMON TANGENT HYPERPLANE AT TWO ORDINARY POINTS -- 1. Derivation of an invariant. -- 2. A projective characterization of the invariant I -- 3. A metric characterization of the invariant I -- CHAPTER II. TWO HYPERSURFACES WITH DISTINCT TANGENT HYPERPLANES AT TWO ORDINARY POINTS -- 4. Derivation of invariants.

5. Projective characterizations of the invariants I J -- 6. Metric characterizations of the invariants I J -- A Projective Invariant of a Certain Pair of Surfaces -- REFERENCES -- Projective Invariants of Contact of Two Curves in Space of n Dimensions -- 1. Introduction -- 2. Derivation of invariants -- 3. Geometrical characterizations of the invariants Ji n~i+2 -- 4. A geometrical characterization of a general invariant Iij -- On Triplets of Plane Curvilinear Elements with a Common Singular Point -- 1. Introduction -- 2. Derivation of an invariant -- 3. Geometrical characterizations of the invariant I -- Invariants of Intersection of Certain Pairs of Curves in n-Dimensional Space -- Introduction -- CHAPTER I. Two Curves Intersecting at an Ordinary Point With Distinct Osculating Linear Spaces. -- 1. Derivation of Invariants. -- 2. Metric and projective characterizations of a general invariant Ii. -- CHAPTER II. Two Curves Intersecting at an Ordinary Point With Distinct Tangents But Certain Common Osculating Linear Spaces. -- 3. Derivation of invariants. -- 4. Metric and projective characterizations of general invariants Ii and Ji. -- Affine Invariants of a Pair of Hypersurfaces -- 1. Introduction -- 2. Derivation of invariants -- 3. Metric and affine characterizations of the invariants -- 4. Discussion -- REFERENCES -- Some Integral Formulas for Closed Hypersurfaces -- Introduction -- 1. Preliminaries -- 2. Proof of the formula (0.2) for r = 0 -- 3. Proof of the formula (0.2) for a general r -- 4. Proofs of Theorems 2 and 3 -- References -- A Theorem on Surfaces with a Closed Boundary -- S 1. Introduction -- S 2. Preliminaries -- S 3. An integral formula -- S 4. Proof of the theorem -- References -- On Differential Geometry of Hypersurfaces in the Large -- 1. Introduction -- 2. Preliminaries.

3. Some integral formulas -- 4. Proof of the theorem -- REFERENCES -- Some Global Theorems on Hypersurfaces -- 1. Introduction -- 2. Preliminaries -- 3. An integral formula -- 4. Proof of Theorems 1 and 3 -- 5. Connection with symmetrizations -- REFERENCES -- A Uniqueness Theorem for Minkowski's Problem for Convex Surfaces with Boundary -- 1. Introduction -- 2. Preliminaries -- 3. Proof of the theorem -- Curvature and Betti Numbers of Compact Riemannian Manifolds with Boundary -- 1. Introduction -- 2. Riemannian submanifolds in Euclidean space -- 3. Differential forms and tensors -- 4. Integral formulas -- 5. Harmonic and Killing vector fields -- 6. Harmonic and Killing tensor fields -- 7. Flatness and deviation from flatness -- A Uniqueness Theorem on Two-Dimensional Riemannian Manifolds with Boundary -- 1. INTRODUCTION -- 2. PRELIMINARIES -- 3. AN INTEGRAL FORMULA -- 4. PROOF OF THE THEOREM -- REFERENCES -- A Uniqueness Theorem on Closed Convex Hypersurfaces in Euclidean Space -- Some Uniqueness Theorem on Riemannian Manifolds with Boundary -- 1. Introduction -- 2. Immersed submanifolds in Euclidean space -- 3. Integral formulas for a pair of immersed manifolds with boundary -- 4. Proofs of Theorems I and II -- 5. Integral formulas for convex hypercaps -- 6. Proof of Theorem III -- REFERENCES -- Isoperimetic Inequalities for Two-Dimensional Riemannian Manifolds with Boundary -- 1. Introduction -- 2. Preliminaries -- 3. Lemmas -- 4. Theorems -- A Note of Correction -- On the Isometry of Compact Submanifolds in Euclidean Space -- Introduction -- S 1. Preliminaries on Algebra -- S 2. Preliminaries on Differential Geometry and Statement of Theorem -- S 3. Integral Formulas -- S 4. Proof of the Theorem -- Curvature and Homology of Riemannian Manifolds with Boundary -- 1. Introduction -- 2. Notations and operators.

3. Harmonic and Killing tensor fields and local boundary geodesic coordinates -- 4. Integral formulas and theorems -- 5. Existence of a constant symmetric tensor -- 6. Riemannian manifolds with zero Ricci curvature -- 7. A general application of Theorems 4.1 4.2 4.3 -- 8. Riemannian manifolds in spaces of constant curvature -- 9. Symmetric manifolds -- References -- Vector Fields and Infinitesimal Transformations on Riemannian Manifolds with Boundary -- Introduction -- 1. Notations and operators -- 2. Lie derivatives and infinitesimal transformations -- 3. Local boundary geodesic coordinates and integral formulas -- 4. Killing vector fields and infinitesimal motions -- 5. Conformal Killing vector fields and infinitesimal conformal motions -- 6. Projective Killing vector fields and infinitesimal projective motions -- REFERENCES -- On the Congruence of Hypersurfaces -- INTRODUCTION -- 1. LEMMAS -- 2. HYPERSURFACES IN EUCLIDEAN SPACE -- 3. INTEGRAL FORMULAS -- 4. THEOREMS -- On the Group of Conformal Transformations of a Compact Riemannian Manifold -- 1. Introduction -- 2. Notations and Formulas -- 3. A Lemma -- 4. Proof of the Main Theorem -- Structures and Operators on Almost-Hermitian Manifolds -- Introduction -- 1. Notations and real operators -- 2. Complex structures and operators -- 3. Proof of Theorem 3.1 -- 4. Realization of the complex operator [] -- REFERENCES -- Affine Differential Geometry of Closed Hypersurfaces -- Introduction -- 1. The affine group and its structural equations -- 2. Frenet affine frames -- 3. The integrability conditions -- 4. The canonical expansion and the fundamental forms -- 5. Affine invariants -- 6. Relations between affine and metric invariants -- 7. Integral formulae -- 8. Theorems -- REFERENCES.

On the Group of Conformal Transformations of a Compact Riemannian Manifold. II -- 1. Introduction -- 2. Lemmas -- 3. Proof of Theorem 5 -- REFERENCES -- Curvature and Characteristic Classes of Compact Riemannian Manifolds -- Introduction -- 1. Higher order sectional curvatures -- 2. Characteristic classes -- 3. Relationships between curvatures and characteristic classes -- References -- The Group of Conformal Transformations of a Compact Riemannian Manifold -- 1. Introduction -- 2. Notations and Formulas -- 3. Proof of Theorem 2 -- Isometries of Compact Submanifolds of a Riemannian Manifold -- Introduction -- 1. Lemmas -- 2. Submanifolds of a Riemannian manifold -- 3. Integral formulas -- 4. Theorems -- On the Group of Conformal Transformations of a Compact Riemannian Manifold. III -- 1. Introduction -- 2. Lemmas -- 3. Proof of Theorem 3 -- References -- Submanifolds of Spheres -- 1. Introduction -- 2. Laplacian of the Second Fundamental Form -- 3. Integral Formulas -- 4. Main Theorems -- Minimal Immersions in Riemannian Spheres -- 1. Introduction -- 2. Notation and formulas -- 3. Proof of Theorem 1.1 -- REFERENCES -- Curvature and Characteristic Classes of Compact Pseudo-Riemannian Manifolds -- Introduction -- 1. Fundamental formulas -- 2. Characteristic classes -- 3. Relationships between curvatures and characteristic classes -- Complex Laplacians on Almost-Hermitian Manifolds -- Introduction -- 1. Notation and real operators -- 2. Complex structures and operators -- 3. Expressions for []'s -- 4. Realization of []'s -- 5. Relationships among []'s -- References -- Conformality and Isometry of Riemannian Manifolds to Spheres -- 1. Introduction -- 2. Notation and formulas -- 3. Lemmas -- 4. Proofs of theorems.

Isometries of Compact Hypersurfaces with Boundary in a Riemannian Space.