From the classical differential equation of Jacobi fields, one naturally defines the Jacobi operator of a Riemannian manifold with respect to any tangent vector. A straightforward computation shows that any real, complex and quaternionic space forms satisfy that any two Jacobi operators commute. In this way, we classify the real hypersurfaces in quaternionic projective spaces all of whose tange...

We introduce an analog of the Maxwell operator on a q-Minkowski space algebra (treated as a particular case of the so-called Reflection Equation Algebra) and on certain of its quotients. We treat the space of ”quantum differential forms” as a projective module in the spirit of the Serre-Swan approach. Also, we use ”braided tangent vector fields” which are q-analogs of Poisson vector fields asso...

The aim of this letter is to indicate the differences between the Rovelli-Smolin quantum volume operator and other quantum volume operators existing in the literature. The formulas for the operators are written in a unifying notation of the graph projective framework. It is clarified whose results apply to which operators and why. Institute of Theoretical Physics, Warsaw University, ul Hoza 69,...

I will discuss results of three different types in geometry and topology. (1) General vanishing and rigidity theorems of elliptic genera proved by using modular forms, Kac-Moody algebras and vertex operator algebras. (2) The computations of intersection numbers of the moduli spaces of flat connections on a Riemann surface by using heat kernels. (3) The mirror principle about counting curves in ...

Projective techniques are unusual and often intriguing for respondents to complete, permitting them to express thoughts and feelings which can be difŽ cult to access by direct and structured questioning. This is achieved by presenting respondents with ambiguous verbal or visual stimulus materials, such as bubble cartoons, which they need to make sense of by drawing from their own experiences, t...

This paper examines a newly created approach to exploring travel motivations, the Travel Career Patterns (TCP) model. Through an analysis of the TCP model, the authors advance travel motivation theory by making three contributions: a refinement of the definition of travel experience; the use and evaluation of essays as a qualitative tool for interpreting travel motives; and an extension of the ...

Misattributions people make about their own affective reactions can be used to measure attitudes implicitly. Combining the logic of projective tests with advances in priming research, the affect misattribution procedure (AMP) was sensitive to normatively favorable and unfavorable evaluations (Experiments 1-4), and the misattribution effect was strong at both fast and slow presentation rates (Ex...

Logically, though not historically, projective techniques must be regarded as a part of the general field of psychological measurement. Projective testing and research may therefore legitimately be studied within the theoretical and methodologicall framework of psychological measurement, always keeping in mind, of course, the problems that are peculiar to projective techniques. Largely as a.. r...