Eduardo Garcia-Rio is a Professor of Mathematics and a member of the Institute of Mathematics of the University of Santiago de Compostela (Spain). He received his Ph.D. degree in 1992 from the University of Santiago de Compostela and is a member of the editorial board of the Journal of Geometric Analysis. His research specialities are Differential Geometry and Mathematical Physics.Peter Gilkey is a Professor of Mathematics and a member of the Institute of Theoretical Science at the University of Oregon (USA). He is a fellow of the American Mathematical Society and is a member of the editorial board of Results in Mathematics, Differential Geometry and Applications, and the International Journal of Geometric Methods to Mathematical Physics. He received his Ph.D. in 1972 from Harvard University under the direction of L. Nirenberg. His research specialties are Differential Geometry, Elliptic Partial Differential Equations, and Algebraic topology. He has published more than 230 research articles and books.Stana Nikcevic is a Professor of Mathematics at the University of Belgrade (Serbia). She received her Ph.D. from the University of Belgrade at the Mathematical Faculty and has been working at the University since 1974. During this period, she also sporadically worked at the University of Banja Luka (Bosnia and Hercegovina) and at the Mathematical Faculty in Kragujevac (Serbia). Her research mainly focuses on Differential Geometry. She has maintained international cooperation and has gone on short visits to the TU Berlin, Charles University Prague, Universitate Pierre et Marie Curie (Paris VI), University of Oregon (USA), and University of Santiago de Compostela (Spain).Ramon Vazquez-Lorenzo is a member of the research group in Riemannian Geometry at the Department of Geometry and Topology of the University of Santiago de Compostela (Spain). He is a member of the Spanish Research Network on Relativity and Gravitation.He received his Ph.D.in 1997 from the University of Santiago de Compostela. His research focuses mainly on Differential Geometry with special emphasis on the study of the curvature and the algebraic properties of curvature operators in the Lorentzian and in higher signature settings. He has published more than 45 research articles and books.

• Basic Notions and Concepts.- The Geometry of Deformed Riemannian Extensions.- The Geometry of Modified Riemannian Extensions.- (para)-Kähler--Weyl Manifolds.

Eduardo Garcia-Rio is a Professor of Mathematics and a member of the Institute of Mathematics of the University of Santiago de Compostela (Spain). He received his Ph.D. degree in 1992 from the University of Santiago de Compostela and is a member of the editorial board of the Journal of Geometric Analysis. His research specialities are Differential Geometry and Mathematical Physics.Peter Gilkey is a Professor of Mathematics and a member of the Institute of Theoretical Science at the University of Oregon (USA). He is a fellow of the American Mathematical Society and is a member of the editorial board of Results in Mathematics, Differential Geometry and Applications, and the International Journal of Geometric Methods to Mathematical Physics. He received his Ph.D. in 1972 from Harvard University under the direction of L. Nirenberg. His research specialties are Differential Geometry, Elliptic Partial Differential Equations, and Algebraic topology. He has published more than 230 research articles and books.Stana Nikcevic is a Professor of Mathematics at the University of Belgrade (Serbia). She received her Ph.D. from the University of Belgrade at the Mathematical Faculty and has been working at the University since 1974. During this period, she also sporadically worked at the University of Banja Luka (Bosnia and Hercegovina) and at the Mathematical Faculty in Kragujevac (Serbia). Her research mainly focuses on Differential Geometry. She has maintained international cooperation and has gone on short visits to the TU Berlin, Charles University Prague, Universitate Pierre et Marie Curie (Paris VI), University of Oregon (USA), and University of Santiago de Compostela (Spain).Ramon Vazquez-Lorenzo is a member of the research group in Riemannian Geometry at the Department of Geometry and Topology of the University of Santiago de Compostela (Spain). He is a member of the Spanish Research Network on Relativity and Gravitation.He received his Ph.D.in 1997 from the University of Santiago de Compostela. His research focuses mainly on Differential Geometry with special emphasis on the study of the curvature and the algebraic properties of curvature operators in the Lorentzian and in higher signature settings. He has published more than 45 research articles and books.

• Basic Notions and Concepts.- The Geometry of Deformed Riemannian Extensions.- The Geometry of Modified Riemannian Extensions.- (para)-Kähler--Weyl Manifolds.

Eduardo Garcia-Rio is a Professor of Mathematics and a member of the Institute of Mathematics of the University of Santiago de Compostela (Spain). He received his Ph.D. degree in 1992 from the University of Santiago de Compostela and is a member of the editorial board of the Journal of Geometric Analysis. His research specialities are Differential Geometry and Mathematical Physics.Peter Gilkey is a Professor of Mathematics and a member of the Institute of Theoretical Science at the University of Oregon (USA). He is a fellow of the American Mathematical Society and is a member of the editorial board of Results in Mathematics, Differential Geometry and Applications, and the International Journal of Geometric Methods to Mathematical Physics. He received his Ph.D. in 1972 from Harvard University under the direction of L. Nirenberg. His research specialties are Differential Geometry, Elliptic Partial Differential Equations, and Algebraic topology. He has published more than 230 research articles and books.Stana Nikcevic is a Professor of Mathematics at the University of Belgrade (Serbia). She received her Ph.D. from the University of Belgrade at the Mathematical Faculty and has been working at the University since 1974. During this period, she also sporadically worked at the University of Banja Luka (Bosnia and Hercegovina) and at the Mathematical Faculty in Kragujevac (Serbia). Her research mainly focuses on Differential Geometry. She has maintained international cooperation and has gone on short visits to the TU Berlin, Charles University Prague, Universitate Pierre et Marie Curie (Paris VI), University of Oregon (USA), and University of Santiago de Compostela (Spain).Ramon Vazquez-Lorenzo is a member of the research group in Riemannian Geometry at the Department of Geometry and Topology of the University of Santiago de Compostela (Spain). He is a member of the Spanish Research Network on Relativity and Gravitation.He received his Ph.D.in 1997 from the University of Santiago de Compostela. His research focuses mainly on Differential Geometry with special emphasis on the study of the curvature and the algebraic properties of curvature operators in the Lorentzian and in higher signature settings. He has published more than 45 research articles and books.

• Basic Notions and Concepts.- The Geometry of Deformed Riemannian Extensions.- The Geometry of Modified Riemannian Extensions.- (para)-Kähler--Weyl Manifolds.