POR MEDIO DE UN ANÁLISIS DE LAS GEODÉSICAS EN UN ESPACIO AXISIMÉTRICO Y ESTÁTICO, OBTENEMOS CONDICIONES SOBRE LA ECUACIÓN DE ESTADO PARA UN FLUIDO PERFECTO ISÓTROPO, P = ! D, CUANDO ÉSTE ES CONSIDERADO COMO LA MATERIA OBSCURA EN LAS GALAXIAS ESPIRALES. LA CONCLUSIÓN PRINCIPAL ES QUE DICHO FLUIDO PUEDE SER EXÓTICO, ES DECIR, CON 1 < ! < 1 3 , COMO SE OBTIENE A ESCALAS COSMOLÓGICAS DENTRO DEL MODELO DE QUINTAESENCIA.AbstractTHROUGH THE GEODESIC ANALYSIS OF A STATIC AND AXIALLY SYMMETRIC SPACE TIME, WE PRESENT CONDITIONS ON THE STATE EQUATION OF AN ISOTROPIC PERFECT FLUID P = !D, WHEN IT IS CONSIDERED AS THE DARK MATTER IN SPIRAL GALAXIES. THE MAIN CONCLUSION IS THAT IT CAN BE AN EXOTIC FLUID (1 < ! < 1=3) AS IT IS FOUND FOR QUINTESSENCE AT COSMOLOGICAL SCALE.THROUGH THE GEODESIC ANALYSIS OF A STATIC AND AXIALLY SYMMETRIC SPACE TIME, WE PRESENT CONDITIONS ON THE STATE EQUATION OF AN ISOTROPIC PERFECT FLUID P = !D, WHEN IT IS CONSIDERED AS THE DARK MATTER IN SPIRAL GALAXIES. THE MAIN CONCLUSION IS THAT IT CAN BE AN EXOTIC FLUID (1 < ! < 1=3) AS IT IS FOUND FOR QUINTESSENCE AT COSMOLOGICAL SCALE.